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THE ELEMENTS 



OF 



NATURAL PHILOSOPHY 



For the Use of Schools and Academies 



¥ 



/ 



BY 



EDWIN J. HOUSTON, A.M., Ph.D. (Princeton) 

Emeritus Professor of Natural Philosophy and Physical Geography in the 

Central High School of Philadelphia ; Professor of Physics in the 

Franklin Institute of the State of Pennsylvania 



REVISED EDITION 





PHILADELPHIA 

Eldredge & Brother 

No. 17 North Seventh StreeT^*^ VW/to htOfcJYttf 



1897 



<oV^| i a; 



& 



0/ 



&S& 






Entered, according to Act of Congress, in the year 1897, by 

ELDEEDGE & BROTHER, 

in the Office of the Librarian of Congress, at Washington. 

H~i ; O^O 



*- 



-# 



WESTCOTT & THOMSON, 
ELECTROTYPERS, PHILADA. 



*" 



-* 



DORNAN, PRINTER, 
PHILADELPHIA. 




r~PHE recent rapid advances in physical science have 
necessitated the preparation of a new edition of " The 
Elements of Natural Philosophy." The author has con- 
sequently prepared a revised edition of the book, in which 
all of the more important advances have been considered. 
- The favorable reception given this book, by the teaching 
profession, has led him to adhere to the general form of 
treatment contained in the original edition. In order to 
obtain the additional space required to treat of new 
topics it has been considered advisable to omit the syl- 
labus and questions for review. 

In view of the increasing importance of the metric 
system, and of the fact that all International physics at 
the present time employ the centimetre-gramme-second 
units, the author has introduced these in connection 
with the English system, the idea being to familiarize 
the student with the metric system, when taken in 
connection with the system he may have to use in prac- 
tice. 

While all portions of the book show the advances 
which have been recently made in the different branches 



iv PREFACE. 

of physics, in none have these advances been so marked 
as in the general subjects of electricity and magnetism, 
which have been thoroughly brought up to date in an 
elementary manner. In all these changes the author has 
endeavored to present the matter in such a form as will 
permit it to be of practical use in the schoolroom. 

The author desires to acknowledge his indebtedness to 
Dr. A. E. Kennelly for assistance in the preparation of 
the new material. 

Philadelphia, October, 1897. 







ra» 



PART I. 

MATTER AND ENERGY. 

.o^oo 

CHAPTER I. 
Matter 9 

CHAPTER II. 
Atoms and Molecules?— Properties of Matter 15 

CHAPTER III. 
The Conditions of Matter 29 

CHAPTER IV. 
Force and Motion 36 

CHAPTER V. 
Gravitation 49 

CHAPTER VI. 

Cohesion and Adhesion, and Properties Peculiar to 
Solids 67 

CHAPTER VII. 

Work, Energy, and Power 82 

v 



VI CONTENTS. 

PART II. 

FLUIDS. 

CHAPTEE VIII. page 
Hydrostatics 101 

CHAPTEK IX. 
Hydraulics 129 

CHAPTEK X. 
Pneumatics • 130 

«K)^00 

PART III. 

SOUND AND LIGHT. 

CHAPTER XI. 
Nature of Wave Motion 145 

CHAPTER XII. 

The Transmission, Reflection, and Refraction of Sound . 152 

CHAPTER XIII. 

The Characteristics of Musical Sounds. — Musical Instru- 
ments , 163 

CHAPTER XIV. 

Light. — Its Nature and Causes 178 

CHAPTER XV. 
The Reflection of Light 188 

CHAPTER XVI. 
The Refraction of Light 195 

CHAPTER XVII. 
Vision and Optical Instruments 204 

CHAPTER XVIII. 
Chromatics , , , . 214 



CONTENTS. vii 

PART IV. 

HEAT AND ELECTRICITY. 

CHAPTER XIX. 

The Nature of Heat 225 

CHAPTER XX. 
Communication of Heat. — Surface Action of Bodies . . . 234 

CHAPTER XXI. 
Heat Units. — Change of State. — Mechanical Equivalent 
of Heat 244 

CHAPTER XXII. 
Electrostatics 260 

CHAPTER XXIII. 
Magnetism 278 

CHAPTER XXIV. 

Electric Current. — Electro-magnetism 286 

CHAPTER XXV. 
Effects of an Electric Current 295 

CHAPTER XXVI. 

The Electric Telegraph and Other Signalling Apparatus. 302 

CHAPTER XXVII. 
Induced E. M. E's. — Dynamos and Motors 307 




THE ELEMENTS 



OF 



NATURAL PHILOSOPHY. 



PART I. 



MATTER AND ENERGY. 



CHAPTER I. 



MATTER. 

1. Experiment 1 .—Fill a tumbler to the brim with water. Quietly 
drop a stone into the water, and observe that some of the water runs out 
of the tumbler. 

Some of the water runs out of the tumbler, because both the stone and 
the water cannot occupy the same space at the same time. The tumbler 
is already filled with water, and when the stone is dropped in, it falls 
to the bottom and causes a volume of water to run out equal to the vol- 
ume of the stone. 

2. Definition of Matter. — Matter is anything which 
occupies space and prevents other matter from occupying 
the same space at the same time. 

If a thing merely occupies space, but does not prevent 
other things from occupying the same space, it is not 
matter. 

All matter occupies space in three dimensions — that is, 

9 



1C NATURAL PHILOSOPHY. 

it has length, breadth, and thickness, or, in other words, 
volume. 

If matter could exist with length and breadth but no thickness, an 
infinite quantity of such matter could be put in a given, limited space, 
such as a cubic inch. The thinnest film of water, or the thinnest leaf 
of gold, has thickness, and, therefore, must possess a definite volume. 

Iron and gold are kinds of matter, since they both 
occupy space and prevent other matter from occupying 
the same space at the same time. 

Air and water are kinds of matter. A body moved 
through air or water does not occupy the same space the 
air or water does, but merely pushes the air or water 
out of its way, and then occupies the space it has thus 
cleared for itself. 

Experiment 2.— Let the sunlight fall on the tumbler filled with 
water. Observe that, though the light fills the tumbler, no water runs 
out. 



Water and light, then, apparently fill the goblet and 
occupy the same space at the same time. Light, therefore, 
is not matter. 

3. The Senses. — We acquire knowledge by means of 
our senses, and by them we become aware of the exist- 
ence of matter, which we can see, hear, feel, taste, or smell. 

All matter, however, is not visible. Air is invisible. 
Heat converts water into invisible vapor. On losing this 
heat, vapor becomes visible as dew, rain, snow, mist, fog, 
or cloud. 

Our senses act as the paths through which impressions are received 
from without ; thus, light entering the eye enables us to see the color 
and form of objects ; by the sense of touch we are enabled to distinguish 
the nature of the surface and the texture of objects ; by the senses of 
taste and smell, we are enabled to select the pleasant and wholesome 
from the disagreeable and noxious ; and, finally, by our hearing, we 
are enabled to understand the thoughts of others when expressed in 
speech. 






MATTER. 11 

4. Substances. Elements. — Different kinds of matter 
are called substances. Iron, wood, water, milk, air and 
vapor are substances. 

Substances are either elementary or compound. 

Elementary substances, or elements, are those which have 
never yet been resolved or separated into more than one 
kind of matter. 

Compound substances are those which are formed by the 
union of two or more elementary substances, and which 
may be resolved or separated into two or more elements. 

We do not know with certainty whether all the so-called elements, 
are actually incapable of division into simpler parts. Thus far they 
have resisted all efforts so to separate them ; but, in the opinion of 
many able scientific men, some of the elements are compound. Indeed, 
in the opinion of some, all the elements are compounds of a single but 
as yet unisolated form of matter. 

Gold is an elementary substance. We cannot, by any 
known means, break it up or separate it into anything but 
gold. Brass is a compound substance, since we can sep- 
arate it into copper and ^inc ; or, by melting copper and 
zinc together in the right proportions we can produce 
brass. 

All known compound substances are formed by various 
combinations of about seventy simple or elementary sub- 
stances. 

Any definite quantity of matter is called a body. Bodies 
may be either large or small ; thus, both the earth, and a 
grain of sand, are bodies, since they are definite quantities 
of matter. 

5. Properties of Matter. — Different kinds of matter 
possess various peculiarities or properties, by means of 
which we are enabled readily to recognize them. Thus, 
gold can be distinguished from marble, because its color 
and its density are different ; gold may also be drawn out 
into wire, or beaten into thin sheets, while marble cannot 
be so drawn or beaten. 



12 NATURAL PHILOSOPHY. 

6. Changes in Matter. — Matter is subject to changes. 
These changes are of two distinct kinds : 

(1) Physical changes, or those which may occur in any 
substance without altering its chemical composition. 

(2) Chemical changes, or those which cannot occur in any 
substance without altering its composition. 

Experiment 3. — Take a piece of steel, such as a common pen, and, 
after examining it carefully, so as to note its peculiarities, rub it once or 
twice with a magnet. The pen will now have acquired a property it did 
not possess before ; it will attract iron filings to it ; but if we again 
examine the pen carefully, we cannot see that it has lost any of the prop- 
erties it previously possessed. This change is a physical change, for the 
substance in undergoing the change has not lost its characteristic prop- 
erties. 

Experiment 4. — Expose the pen for some time to damp air. 
Observe that it becomes covered with a brown rust, which is formed by 
oxygen, a substance in the air, combining with the iron of the pen. 
Observe that the rust so formed resembles neither of the things out of 
which it was formed, since one of them was the iron of the pen itself, and 
the other, an invisible gas. This change is a chemical change, since both 
bodies have lost the properties or peculiarities by which they are gener- 
ally recognized. 

7. Physics or Natural Philosophy, and Chemistry. 

— Natural Philosophy or Physics is the name given to the 
study which considers the causes and effects of the physi- 
cal changes which take place in matter. 

Chemistry is the name given to the study which considers 
the causes and effects of the chemical changes which take 
place in matter. 

8. Phenomenon.— Anything which happens in the 
ordinary course of nature is called a phenomenon. 

As commonly used, the word phenomenon means some- 
thing unusual or strange ; but as used in science, it means 
anything which happens naturally. The fall of a leaf, the 
shining of the sun, the fall of a raindrop, and the growth 
of a plant, are called phenomena. 

9. Cause and Effect. — Nothing happens of itself. All 
natural phenomena are produced by certain causes; for 






MATTER. 13 

example, unsupported bodies fall : here all we see is the 
effect, namely, the motion. The cause of the motion is the 
attraction which the earth has for the body. 

An effect may itself be the cause of some succeeding 
effect ; thus, the body, in falling to the earth, may give 
some of its motion to another body which it strikes, and 
this effect may in turn be the cause of some subsequent 
effect, and so on indefinitely. 

The causes w 7 hich produce natural phenomena can be 
traced to the action of certain forces, one of the most 
important of which is gravity. 

10. Natural Law.— The relation between cause and 
effect is constant and invariable. The same cause, acting 
in the same way, always produces the same effect. Thus, 
unsupported bodies always fall to the earth ; a steel pen 
rubbed against a magnet always becomes magnetic, the 
same pen, unless specially protected, always becomes 
covered with rust when exposed for some time to damp 
air. 

When, by observation we discover the cause of any 
natural phenomenon, and ascertain the order in which 
cause and effect follow each other, this order, expressed in 
language, forms what is called a natural law. 

Natural philosophy has for its object the study of natural 
laws. This definition, it will be seen, embraces the study 
of all natural phenomena ; but natural philosophy is gen- 
erally restricted to the study of the laws concerning phys- 
ical changes. 

11. Method of Study. — There is only one way in 
which we can discover natural laws, and that is by observa- 
tion. If we wish to know what effect will follow a certain 
cause, we must make the trial, and observe what happens. 
If, after repeated careful trials or experiments, we obtain 
the same effects, we may conclude that we have discovered 
the law. 



14 NATURAL PHILOSOPHY. 

12. Energy is the power of producing phenomena or 
doing work. Natural phenomena never occur of them- 
selves. They are always due to energy acting on matter. 
Whenever matter is set into motion or whenever the 
amount or direction of its motion is changed, energy is 
expended, or work is done. 

A log of wood cannot be sawn or cut unless energy is 
expended or work is done. A ball is not driven from a gun 
until the force of the gunpowder or other explosive, 
causes energy to be expended on it. Water cannot pass 
off into invisible vapor until the heat-energy from the sun 
or from some other source acts upon it. 

13. The Indestructibility of Matter. 

Experiment 5. — Burn a piece of paper. Observe that the paper 
disappears, and that the heat developed is apparently lost. 

In reality there has been no loss. By the process of burning, the 
paper has been changed into invisible gases. The quantity of matter in 
the paper has not been changed by burning. The heat liberated has 
acted on the surrounding matter and produced changes therein. 

There exists in the universe a definite quantity of mat- 
ter. During the changes that occur, the quantity of matter 
can neither be increased nor diminished. Matter may dis- 
appear in one form but only to reappear in some other form. 







CHAPTER II. 

ATOMS AND MOLECULES. PROPERTIES OF MATTER. 



14. Experiment 6.— Fill two tumblers, one with water and the 
other with dry sand. Observe, that even to the sharpest vision, the 
water appears to fill the entire space within the tumbler; or, in other 
words, the water appears to be absolutely continuous, while the sand does 
not fill the entire space within the tumbler, but is distinctly granular, and 
contains spaces between the separate grains. 

15. Atoms. — When examined by the most powerful 
microscope, the water in the tumbler appears to be 
absolutely continuous. Nevertheless, there are ample 
reasons for believing that water, like all matter, is not 
continuous but is granular; or is composed of exceed- 
ingly small separate quantities of matter called atoms. 

Atoms are believed to be unalterable in their size and 
shape ; they cannot be cut or scratched by the sharpest 
tools ; bent, twisted or flexed by the most powerful forces ; 
and are not affected by heat or cold. 

It is easy to cut a piece of gold leaf, or tin-foil into exceedingly small 
pieces with a pair of scissors or with a sharp knife. When these pieces 
are so small as to render it difficult to further divide them, it is easy by 
placing one of them under a microscope capable of magnifying, say 500 
times, to cut it into 500 pieces, and if the magnifying power of the mi- 
croscope be increased, it is easy to carry the subdivision still further. 

The particles of gold or of tin obtained in this manner present all the 
appearances peculiar to gold or to tin. They have the same color and 
lustre, and their hardness and other peculiarities are the same. Though 
exceedingly minute these particles are not atoms, but in all probability 
consist of many millions of atoms. 

If we could continue dividing and subdividing the particles of the 
gold, or of the tin, we would finally reach the atoms which are believed 
to be indivisible. 

15 



16 NATURAL PHILOSOPHY. 

Each of the seventy different kinds of elementary sub- 
stances or elements is formed of the same kind of atoms. 
It is believed that the atoms of each kind of elementary 
substance have the same size and weight, but that the 
atoms of different kinds of elementary substances have 
different sizes and weights ; thus, all atoms of iron are of 
the same size and weight, no matter from what part of the 
world the iron may come. In the same manner, all atoms 
of gold are of the same size and weight ; but the atoms of 
iron are neither of the same size nor of the same weight 
as the atoms of gold. 

16. Molecules and Masses. — It is believed that atoms 
do not exist in a free state in ordinary matter, but under the 
influence of the attractions or affinities they possess for 
one another they unite in definite groups called molecules. 
Though larger than atoms, the molecules are too small to 
be seen even by the aid of the most powerful microscope. 

Atoms are not infinitely small, but possess definite size ; 
i. e., they have length, breadth, and depth, or occupy space 
in three directions. 

Kelvin estimates that if a drop of water were magnified to the size 
of the earth, the molecules would be larger than small shot, but smaller 
than cricket balls. The atoms would, therefore, be still smaller. 

It has been estimated that a cubic centimetre (equal to about the one- 
sixteenth part of a cubic inch) of air at ordinary pressure and temperature 
contains twenty quintillions of molecules, i. e., 20,000,000,000,000,000,000; 
or, as it is sometimes written, 2 x 10 19 , or 2 followed by 19 ciphers. 

Neither the atoms nor the molecules touch one another, 
but are separated by spaces called pores. All matter is, 
therefore, granular, the smallest particles being the atoms 
of which the matter is composed. The next smallest parti- 
cles of ordinary matter are the molecules or groups of atoms. 

Molecules may consist either of atoms of the same ele- 
ment, or of atoms of different elements ; that is, molecules 
may be either elementary or compound. 

The number of separate atoms in a molecule varies with 
the kind of atoms that unite to form the molecule. A 



ATOMS AND MOLECULES. 17 

molecule of water has three atoms ; a molecule of ordi- 
nary sugar has forty-five atoms ; and a molecule of aniline 
blue has seventy-two atoms. 

A molecule of water consists of one atom of oxygen combined with 
two atoms of hydrogen. Should one of the hydrogen atoms be taken 
away from the molecule of water, there would be left an incomplete 
group of atoms, consisting of one atom of hydrogen and one atom of 
oxygen. Such a group of atoms would not have its attractions com- 
pletely satisfied, since it could combine with another atom like hydro- 
gen. It forms what is called a radical. 

17. Varieties of Attraction. — Besides the attractions 
or affinities that atoms possess for one another, as a result 
of which they unite and form molecules, the molecules 
also possess attractions for one another and form groups 
of molecules called masses. The separate masses also pos- 
sess mutual attractions. 

There are, therefore, three kinds of attraction : 

1. Atomic attraction; or chemical affinity r , whereby the 
atoms unite and form groups of atoms called molecules. 

The rusting of iron, the burning of coal, and the explo- 
sion of gunpowder are examples of atomic attraction. 

2. Molecular attraction, whereby the molecules come 
together and form what are called masses. 

Molecular attraction is called cohesion when it exists 
between molecules of the same kind, and adhesion when 
it exists between molecules of different kinds. 

The molecules of a piece of chalk cohere to one another, 
but adhere to the molecules on the surface of a blackboard. 

3. Molar or mass attraction, which exists between differ- 
ent masses of matter. 

Mass attraction is generally known as the attraction of 
gravitation, or, more simply, as gravity. 

An unsupported body falls to the earth by reason of 
molar attraction or gravity. 

18. Essential and General Properties of Matter. — 
There are certain properties which are possessed ex- 
clusively by the atoms of matter; there are other proper- 

2 



18 NATURAL PHILOSOPHY. 

ties which are possessed in common by atoms and mole- 
cules, and still other properties which are possessed 
in common by atoms, molecules, and masses. 

Properties possessed only by the atoms, may be called 
the essential properties of matter. 

Properties possessed in common by the atoms, molecules, 
and masses, or by the molecules and masses, are called the 
general properties of matter. 

There are still other properties that are possessed only 
by particular kinds of matter. These may be called spe- 
cific or particular properties of matter. 

19. The Essential Properties of Matter, or those 
possessed by the atoms only, are 

1. Impenetrability, or that property of the atom by which 
it resists penetration or entrance by any other body. 

When a nail is driven into a board, or a stone is dropped 
into water, the atoms are not penetrated, but masses of 
molecules are merely pushed aside. 

2. Indivisibility, or that property of the atom by which 
it resists being cut or divided into smaller particles. The 
word atom means that which cannot be cut. 

Indivisibility arises from the impenetrability of the atom. 

3. Indestructibility. — If the atom can neither be pene- 
trated nor divided, it cannot be destroyed. 

20. The General Properties of Matter, possessed in 
common by atoms, molecules, and masses, are extension, 
inertia, mobility, and weight. 

The general properties possessed in common by mole- 
cules and masses, are divisibility, porosity, compressibility, 
and expansibility. 

21. Extension is that property by virtue of which mat- 
ter occupies space in three directions; viz., in length, 
breadth, and thickness. 

Though as we have seen, the atoms are exceedingly small, yet they 
possess definite size ; that is, they have extension, or occupy space in the 



ATOMS AND MOLECULES. 19 

three dimensions of length, breadth, and thickness. Extension is also 
necessarily possessed by the molecules and the masses, and is, therefore, 
a general property of matter. All matter possesses extension in the 
three directions of length, breadth, and thickness, or, in other words, 
all matter possesses volume. 

22. Units of Measurement. — In the United States 
and Great Britain the dimensions of a body, that is its 
length, breadth, and thickness, are measured in certain 
units called inches, feet, yards, and miles. In other parts 
of the world, and in scientific writings generally, dimen- 
sions are measured in metres, or in decimal multiples or 
submultiples of a metre. 

The metric system of length originated in France. The 
unit of length, the metre, is equal to one-forty-millionth 
part of a circumference of the earth taken through the 
poles and through Paris ; i. e., of the distance between the 
Equator and the North Pole. A metre is equal to 39.3698 
inches ; or, in round numbers, 39.37 inches. 

The values of the principal English and French units 
are given below. 1 It will be noticed that the measures 
of surface are obtained by squaring the measures of length : 

English Measure. 

Measures of Length. Measures of Surface. Measures of Volume. 

12 in. make one ft. 144 sq. in. = 1 sq. ft. 1728 cub. in. = 1 cub. ft. 

3 ft. " " yd. 9 sq. ft. = 1 sq. yd 27 cub. ft. = 1 cub. yd. 

1760 yds., or 5280 ft, 
make one mile. 

French Measure. 

Measures of Length. 

1 metre equals 39.37 English inches or 3.281 ft. 

1 decametre., or 10 metres " 393.7 " " 

1 hectometre, or 100 metres " 3937. " " 

1 kilometre, or 1000 " " 39370. " " or 1093.6 yds. 

1 decimetre, or T \ " " 3.937 " " 

1 centimetre, or T ^ " " .3937 " " 

1 millimetre, or T oVo " " -03937 " " or & in. nearly. 



20 NATURAL PHILOSOPHY. 

thus, one square foot equals 12 inches X 12 — 144 square 
inches ; one square yard equals 3 feet X3 = 9 square feet. 
Similarly, one square metre equals 1 metre X 1 = 1 square 
metre ; or, since 1 metre = 39.37 inches, one square metre 
== 39.37 inches X 39.37 = 1550 square inches. 

The measures of volume are obtained by cubing the 
measures of length ; thus, one cubic foot equals 1 ft. X 1 X 
1, or, 12 inches X 12 X 12 = 1728 cubic inches. Similarly, 
one cubic metre = 1 metre X 1 X 1, or 39.37 inches X 
39.37 X 39.37 = 61023 cubic inches, approximately. 

A centimetre is approximately four-tenths of an inch. 

In the French system, the litre, which is generally taken 
as the standard unit of volume, is the volume of a cube, 
the length of the edge of which is one decimetre, or ten 
centimetres. 

The names and values of the French units of surface 
and of volume, as well as the decimal divisions of the 
litre, are given below. 1 

1 Measures of Area or Surface. 

1 square metre equals 1550. sq. in., or 10.764 sq. ft. 

1 square decimetre equals . . . 15.5 " 

1 square centimetre " ... .155 " 

1 square millimetre " ... .00155 " 

Measures of Volume. 
1 cubic metre equals . . . 61023. cub. in., or 35.32 cub. ft. 

1 cubic decimetre, or litre equals 61.02 " 

1 cubic centimetre equals .06102 " 

Values of English in French Units. 
1 inch = 2.54 centimetres nearly. 
1 foot = 30.48 centimetres nearly. 
1 yard = 91.44 centimetres nearly. 
1 mile = 160900 centimetres nearly. 

Siibdivisions of a Litre. 
1 millilitre - .06102 cubic inch. 

1 centilitre — .6102 cubic inch. 

1 decilitre = 6.102 cubic inches. 

1 litre = 61.02 cubic inches. 



ATOMS AND MOLECULES. 



21 



Figure 1, represents the actual length of the decimetre, and Fig. 2, 
the actual length of four inches. Since a decimetre equals 3.937 inches, 
it is but a trifle shorter than four English inches. From A to B, is one 
decimetre ; from A to a, is one centimetre, of which there are ten in 
one decimetre, or in the whole length of A B. From A to 6, is one 
millimetre, of which there are ten in every centimetre. 

From Cto D, is four English inches ; from Cto a, is one inch ; from 
C to b, is one-tenth of an inch. There are about 
twenty-five millimetres in one inch. 

1 micron = the one-millionth part of a metre, or the 
one-thousandth part of a millimetre. The micron is 
much used as a unit of length in microscopy ; the 
smallest visible particle being about the tenth of a 
micron in size. 

23. Inertia. — A body never begins to 
move, never stops moving, nor changes the 
direction in which it is moving, unless force 
of some kind acts upon it. In other words, 
matter can do nothing of itself towards 
changing its condition, either of rest or of 
motion. 



If we attempt to move a comparatively large body 
from a state of rest, as, for example, a wheel capable 
of revolving freely on an axis, we shall find it neces- 
sary to exert our strength for some time before we 
can get the wheel moving rapidly ; that is, we find 
that a body at rest apparently offers a resistance to 
changing its state of rest. On the other hand, when 
the wheel has been set in motion, we shall be obliged 
to exert our strength, but this time in the opposite 
direction, before we can bring the wheel to rest 
again ; that is, we find that a body in motion ap- 
parently offers a resistance to changing its state or 
condition of motion, just as a body at rest offers a 
resistance to changing its condition of rest. 

By the inertia of matter is meant its tend- 
ency to continue in whatever condition it may be, whether 
at rest or in motion, until some force acts upon it. It fol- 
lows, from the property of inertia, 



^ ^ 



= a 



.= g - 



do 



22 NATURAL PHILOSOPHY. 

1. That a body at rest will continue at rest for ever, unless 
some force acts upon it 

2. That a body in motion will continue in motion for ever, 
unless some force acts upon it 

It is easy to understand that a body at rest will continue at rest for 
ever, until acted upon by some force, since such is a matter of common 
observation. But it is difficult, at first, to believe that the same thing 
is true of a body in motion. For example, we know that a stone thrown 
straight up in the air will not continue moving upward forever. In 
reality, it moves more and more slowly every moment, and at last en- 
tirely stops, and begins to fall back to the earth. But in this case 
the stone does not stop its own motion. It is stopped because the 
earth is constantly pulling it down towards it, and because the air is 
resisting its motion. Could we go out into empty space, beyond the 
influence of any other force, and throw the stone in any direction, it 
would continue moving for ever in a straight line in that direction, 
since, as it is inert, it has no more power to stop its motion than it 
has to begin to move. 

The earth moves through the apparently empty space 
around the sun, where there is nothing to stop its motion, 
at a rate of more than a million and a half miles per day. 
It must, therefore, continue moving for ever, unless stopped 
by a sufficiently powerful force. 

Perpetual motion, in the case of a body like the earth moving through 
a space in which it meets no resistance, necessarily exists from the fact 
that the moving body has inertia. On the earth the perpetual motion 
of a machine, as ordinarily understood, is an impossibility, since the 
motion of the machine is resisted both by the friction of its supports, 
and of the air, or other medium, in which it is moving. 

24. Examples of Inertia. — When a train of cars 
begins to move, some time is required before full speed is 
attained, on account of inertia. When, however, the train 
has attained this speed, considerable force at the brakes 
must be exerted to stop it. 

Since energy is indestructible, before a moving body 
can be brought to rest, it must expend an amount of 
work equal to that which was done on it to cause it to 






ATOMS AND MOLECULES. 23 

move. Cannon-balls owe their great destructive power to 
the fact that they have been set in motion by a powerful 
force; viz., by the explosion of gunpowder, hence they 
overcome considerable resistance before stopping. 

If we jump from a rapidly moving car, we are likely to 
fall, because, on reaching the ground, the motion of our 
feet is stopped, while the rest of our body continues to 
move forward by its inertia. Again, a running jump will 
carry us much farther than a standing jump, because, if 
we first run rapidly in the direction in which w r e w T ish 
to jump, the motion thus given to the body will help to 
carry it in that direction. 

Experiment 7. — Stand a book upright on its end on a sheet of 
paper. Pull the paper slowly and the book can be moved without falling. 
Observe that motion is gradually imparted to the book. While the book 
is moving, suddenly stop moving the paper. Observe that the book will 
fall forward, since its top keeps on moving after that part resting on the 
paper has stopped. 

Experiment 8. — Pull the paper quickly on starting. Observe that 
the book falls backward, because the part resting on the paper is moved 
forward before the top commences to .move. 

25. All Matter Possesses Inertia. — All matter, 
whether living or without life, possesses inertia. 

We are conscious of having to exert our strength before 
we can move about from place to place. Thus, we move 
an arm by means of its muscular force. When we set 
our bodies in rapid motion, as in running down a hill, we 
find it necessary to exert considerable force in order to 
stop suddenly. 

26. Mobility is that property of matter which enables 
it to be moved or to change its place when acted on by 
any force. 

Since the earth is continually rotating on its axis, and revolving 
around the sun, it is clear that nothing on the earth is ever actually at 
rest. We usually say, however, that a body is at rest when it is not 
changing its position in relation to neighboring bodies. 



24 NATURAL PHILOSOPHY. 

Besides the more apparent motions that occur around us, like the 
flowing of a river, the flight of a bird, or the fall of a stone, there 
are other motions too minute to be seen. The molecules in all 
forms of matter are never at rest, but are in rapid motions to-and- 
from one another. These motions cause various phenomena of heat 
and light. 

27. Resistance to Motion. — A body moving through 
air or water can advance only by pushing the air or water 
out of its way. Since both air and water possess inertia, 
they cannot move themselves out of the way, and, there- 
fore, require force to act upon them. This force is de- 
veloped by the moving body, and diminishes its energy 
of motion. Resistances of this kind are called fluid resist- 
ances, and are impediments to motion. 

If the resistance of the air did not retard the fall of a raindrop, its 
velocity on reaching the earth would be sufficient to render it as fatal to 
the person it struck as a bullet shot from a rifle. 

28. Friction. — When bodies are slid or are rolled over 
one another, they meet another resistance or impediment 
to motion. Even the smoothest surfaces we can obtain 
are marred by irregularities. When one body is slid 
or rolled over another, the projections of the one fitting 
into the depressions in the other, cause a resistance to 
motion. Besides the irregularities of the surface, when- 
ever two bodies are brought near each other, they attract 
or tend to hold on to each other. The resistances to mo- 
tion produced in this way are called frictions. 

Friction results either by sliding or by rolling one body 
over another. Rolling friction is less than sliding friction 
because, in rolling, the elevations of one of the contact sur- 
faces are lifted out of the depressions in the other, while 
in sliding they are moved bodily over one another. In 
sliding friction, the force required to start the body is 
greater if it has been resting on the other body for some 
time. 



ATOMS AND MOLECULES. 



25 



Experiment 9.— Insert a screw-hook into the side of a brick. Place 
the brick flat on a table. Attach one end of a string to the hook, and pass 
it over a small pulley, as shown in Fig. 3. Add weights to the end of the 
string to start the brick moving. Disregarding the friction of the pul- 
ley, these weights equal the starting friction between the brick and the 
table. 




Fig. 3.— Friction Apparatus. 

The friction between two surfaces increases with the 
pressure between them. 

Experiment lO. — Place a second brick on the first. The pressure on 
the table is doubled. Observe that the weight required to start the two 
bricks in motion will be about twice as great as in the first case. 

Within certain limits, friction is independent of the 
area of contact surfaces. Thus, if the brick used in ex- 
periments 9 and 10 be placed upon the table on its edge, 
instead of on its face, the same weight will be required 
to start it ; for, although the surfaces in contact are now 
smaller, the weight on each square inch of surface is 
greater. 

The amount of friction between two surfaces depends 
upon the nature of the surfaces. In general, friction is 
greater between surfaces of the same kind than between 
surfaces of different kinds. 

Friction is diminished by filling the irregularities of the 
surfaces with grease or oil. 

A body is slippery if it produces but little friction when 
moved over another body. 



26 NATURAL PHILOSOPHY. 

29. Weight. — The attraction which the earth exerts 
for any quantity of matter is called its weight. 

All matter on the surface of the earth possesses weight. 

30. Divisibility is that property of matter by which it 
may be separated or divided into smaller parts. 

Masses are divisible into smaller masses. They are also 
divisible into molecules. Molecules are divisible into 
atoms. Atoms, however, cannot be divided. They are 
the smallest particles into which matter can be divided. 

The following examples will show the wonderful extent to which it 
is possible to carry the division of matter: Gold can be beaten into 
leaves so thin that it would take three hundred thousand placed one 
upon the other, to make a pile one inch thick, and yet, each of these 
leaves may be cut into very small pieces. 

A grain of musk will for years continue to give off odorous particles 
to the air around it, without decreasing perceptibly in weight. 

A very small quantity of certain coloring matters will give a decided 
tint to a large quantity of water. Now, since the water so colored may 
be divided into a great number of parts, in each of which the color 
is distinctly visible, the quantity of coloring matter in each part must 
be exceedingly minute. 

The microscope has revealed to us the existence of organisms so small 
that millions of them can easily move in the space of a cubic inch with- 
out touching one another. 

31. Porosity. — Neither the atoms which form molecules, 
nor the molecules which form masses, remain in contact 
with one another, but are separated by spaces called pores. 

Pores are either — 

1. Inter-atomic; i. e., between the atoms that form the 
molecules. 

2. Inter-molecular ; i. e., between the molecules that form 
the masses. 

3. Inter-molar; i. e., between the particles or little masses 
that form the greater masses, 

The inter-molar pores are the largest, and may be readily 
seen, as in most woods, or in sponges. 



ATOMS AND MOLECULES. 



27 



The inter-molecular pores are so small that they cannot 
be seen, even with a powerful microscope. 

The inter-atomic pores are probably still smaller. 

All matter is porous, that is, it possesses inter-atomic and 
inter-molecular pores ; some matter possesses also inter- 
molar pores. 

The inter-molecular pores are largest in gases, smallest in 
solids, and of intermediate size in liquids. 

Though inter-molecular pores cannot be seen, yet we 
know that they exist, because matter, when in mass, is 
compressible, expands on being heated and contracts on 
being cooled. 

Experiment 11.— Fill a tumbler to the brim with alcohol. Slowly 
place in the alcohol several handfuls of loose, absorbent cotton. Observe 
that though a bulk of the cotton several times the bulk of the alcohol is 
put in the already full tumbler of alcohol, yet none of the alcohol runs out. 

Here the molecules of the alcohol and absorbent cotton mutually pene- 
trate each other's inter-molecular pores. 

Experiment 12.— Slowly pour a quantity of granulated sugar into 
a tumblerful of warm water. Observe that no apparent increase in 
volume occurs. 

Here the sugar molecules penetrate the inter-molecular pores between 
the water molecules. 

32. Expansibility. — Matter contracts or decreases in bulk 
by a loss of heat, and expands or in- 
creases in bulk by an increase of 
heat. Generally, gases expand more 
than liquids, and liquids more than 
solids, with the same increase of heat. 



. Experiment 13.— If an empty glass bot- 
tle be held mouth downwards, in a plate of 
water, as shown in Fig. 4, so that the mouth is 
just under the water, and the hand be made 
to cover as much of the outside of the bottle 
as possible, the heat from the hand will cause 
the air inside the bottle to expand, so that the 
bottle will no longer be able to hold it all, and the air will be seen to 
escape from the mouth of the bottle in bubbles. 




Tig. 4,— Expansion of Air, 



28 NATURAL PHILOSOPHY. 

Problems. 

ooj^o* 

1. The polar circumference of the earth through Paris is approxi- 
mately 24,860 miles. From this calculate the value of a metre in 
feet. Arts. 3.2815 feet, 

2. Calculate your height in metres. 

3. The summit of Mount Washington, the highest elevation in 
the State of New Hampshire, has an altitude of 1916 metres above 
mean tide level. Find this altitude in feet. 

Arts. 6286 feet (approximately). 

4. The gauge of most railroads is 4 ft. 8| ins. Express this in 
metres. Ans. 1.435 metres. 

5. The Krag-Jorgensen repeating-rifle, adopted for the U. S. 
army, has a calibre of 0.3 inch, and imparts an initial velocity of 
2000 feet per minute to its projectile. Express the calibre in 
metres and millimetres, and the initial velocity in metres per 
second. Ans. Calibre, 0.00762 metre. 7.62 millimetres. Initial 
velocity, 609.6 metres per second. 

6. The river span of the Brooklyn bridge is 1595 ft. 6 ins. Ex- 
press this in metres. Ans. 486.3 metres. 

7. The area of land upon the surface of the globe is approxi- 
mately 137.3 million sq. kilometres. Express this area in square 
miles. Ans. 53,000,000 sq. miles (approximately). 

8. The breadth of a red corpuscle, in normal human blood, 
varies between the -^tnt and the 3^Vtt P ar ^ °f an inch. Express 
this range in centimetres. 

Ans. 0.0007258 to 0.0007938 centimetres. 

9. The amount of blood in the body of a full-grown man being 
say 680 cubic inches, and there being approximately five millions 
of red blood-corpuscles in a cubic millimetre, find the number of 
red blood-corpuscles in his body. Ans. 55,700,000,000,000. 




CHAPTER III. 

THE CONDITIONS OF MATTER. 



33. States or Conditions of Matter. — 

Experiment 14. — Gradually heat a lump of ice in a suitable glass 
vessel. Observe that the ice melts, and, if the heat be continued, the 
water boils and passes off as vapor as soon as a certain temperature is 
reached. 

If water vapor is allowed to pass into an extremely large empty space, 
it will expand and fill the space, assuming the condition known as the 

ultra-gaseous. 

Water may, therefore, exist— 

1. As a solid in the form of ice. 

2. As a liquid in the form of water. 

3. As an invisible vapor in the form of steam. 

4. In the ultra-gaseous state. 

All matter may exist in the four conditions above 
named; viz., the solid, the liquid, the gaseous, and the 
ultra-gaseous. 

The change of liquids into gases or vapors by the action 
of heat is called vaporization. 

When any quantity of vapor loses the heat which con- 
verted it into vapor, it again becomes a liquid. This pro- 
cess is called liquefaction or condensation. 

When a gas is subjected to pressure, its molecules are 
forced together and their freedom of motion reduced. 

If the temperature is not too high, this pressure, when 
sufficiently great, will change the gas into a liquid. Gases 

29 



30 NATURAL PHILOSOPHY. 

may also be liquefied by cold. Generally both cold and 
pressure are employed in their liquefaction. 

As a rule, vapors are liquefied by mere loss of heat, while 
gases require both loss of heat and compression, in order to 
bring their molecules sufficiently near one another to be- 
come liquids. 

Until quite recently, a number of gases had never been liquefied by 
cold or pressure. These were called the incoercible or permaneM gases. 
By subjecting them to intense cold and pressure combined, these too 
have recently been changed into liquids. There are, therefore, no gas- 
eous substances that may now be considered as incoercible. 

34. The Kinetic Theory of Matter. — It is believed 
that the molecules of matter are never at rest, but that in 
the densest solids, as well as in gases and ultra-gases, they 
are moving to-and-fro towards and from one another with 
exceeding rapidity. 

The lengths of the paths through which the molecules 
move, are greater in liquids than in solids, still greater 
in gases, and greatest of all in ultra-gases. 

The molecules, in their to-and-fro motions, frequently collide or strike 
against one another. The effect of these collisions is to change both 
the direction and the velocity of their motion. The collisions are 
more frequent in solids than in liquids, and in liquids than in gases. 
In solids, the molecules, in their to-and-fro motions, do not change their 
relative positions, adjacent molecules remaining adjacent molecules. In 
liquids and in gases, however, the molecules slip over or move past one 
another, so that adjacent molecules do not remain adjacent molecules. 
Thus, taking the students in a school-room to represent individual mole- 
cules in one plane of a solid, if they moved to-and-fro in their seats 
without changing their seats, they would always retain the same relative 
positions. The same students at play in a playground, would represent 
the condition of molecules in one plane of a liquid or gas ; for, here, the 
students would not retain their relative positions during their move- 
ments. 

35. The Molecular Forces. — The molecules in their 
to-and-fro motions are kept at certain average distances 
from one another, by the action of two equal and opposite 



THE CONDITIONS OF MATTER. 31 

molecular forces, one of which, the force of molecular attrac- 
tion, tends to draw the molecules together ; the other, the 
force of molecular repulsion, tends to keep them apart. 
Molecular repulsion is caused by the action of heat. 
The cause of molecular attraction is unknown. 

The different conditions of matter, the solid, the liquid, the gaseous, 
and the ultra-gaseous, result from the different degrees with which these 
attractive and repulsive forces act on the molecules, and the consequent 
difference in the freedom of movement possessed by these molecules. 

36. Solids. — In solids, molecular attraction is stronger 
than molecular repulsion; consequently, the molecules 
in their to-and-fro motions resist any force tending to 
change their relative positions. Moreover, the paths 
through which the molecules move are limited. 

Solids may take any shape because their molecules 
strongly cohere. 

The intensity of molecular attraction varies in different 
solids. A piece of paper, or a match stem, may easily 
be pulled into smaller pieces, but, if we take a piece of 
sheet iron, no thicker than the paper, and try to pull it 
to pieces, we shall find that it will require a much greater 
force than can be exerted by the unaided hands. 

A steel wire, so thin as to be practically invisible at a 
distance of several yards, may be strong enough to hold 
a man's weight. 

In soft wax or butter, the molecules are held together 
so feebly that but little force is required to change 'the 
shape of the mass. These substances in some respects 
resemble liquids. 

37. Fluids. — Substances whose molecules move freely 
over one another are called fluids. There are two kinds of 
fluid substances ; viz., liquids and gases. 

38. Liquids. — In liquids, the force of molecular attrac- 
tion is weaker than in solids. The molecules are not held 
so strongly together, and move through longer paths. 



32 NATURAL PHILOSOPHY. 

Moreover, when acted on by any force, they can easily 
move or slide over one another. 

From the great freedom of motion of their molecules, 
liquids possess no definite shape, but assume that of the 
vessel in which they are kept, except on their free or upper 
surface, which is sensibly horizontal or level. A quantity 
of water poured into a bottle will take the shape of the 
inside of the bottle, and will keep that shape as long as it 
continues in the bottle ; but if poured into a cup, plate, or 
tumbler, it will at once take the shape of the inside of 
the cup, plate, or tumbler. 

39. Mobile and Viscid Liquids. — The strength of 
molecular attraction varies in different liquids. In some 
liquids the molecules, in their to-and-fro motions, are at- 
tracted to one another with much greater force than in 
others, and, therefore, tending to retain their relative 
positions, do not move or flow over one another so 
readily. 

In molasses or tar, the molecules do not flow over 
one another as readily as in alcohol or ether, because 
the molecules of molasses or tar are held together with 
greater force than are the molecules of the alcohol or 
the ether. 

Liquids, like molasses or tar, in which the molecules 
do not flow over one another readily, are called viscid or 
viscous liquids. Liquids like alcohol or water, in which 
the molecules flow over one another readily, are called 
mobile liquids. 

All liquids possess some viscosity, because, although the molecules 
are moving freely, yet they are within the influence of each other's 
attractive forces. A stream of liquid does not readily break into drops, 
and while flowing, the molecules hinder each other's motions by their 
mutual attraction. 

Some solids, like soft butter, can scarcely be distin- 
guished from liquids. On the other hand, some liquids, 






THE CONDITIONS OF MATTER. 33 

like very thick tar, are difficult to distinguish from solids. 
The solid condition often passes imperceptibly into the liquid 
condition. 



Some solids, such as the metals, when subjected to sufficient pressure, 
exhibit many of the phenomena of flow. In the process of wire-draw- 
ing, a stout bar of cold iron or copper may be drawn, without fracture, 
into a wire many hundred times the length of the original bar. 

A disc of metal, put under a powerful coining press, is caused by the 
pressure, to flow into all the cavities of the die, thus accurately as- 
suming the precise impression. Heavy blocks of ice or stone, when 
subjected to long continued pressure, may be considerably bent or flexed 
without fracture. 

40. Influence of the Pressure of the Air on Liquids. 

— Were it not for the pressure of the air, many bodies 
which are now liquids would become gases. Water and 
many other liquids, when placed in a space from which 
all the air has been removed, will turn into the gaseous 
state. Gaseous bodies that are formed from liquids in 
this way, or by the direct action of heat, are called 
vapors. 

In many liquids the forces of molecular attraction and repul- 
sion are not in equilibrium, until the pressure of the atmosphere 
adds its force to that of attraction. 

In gases the to-and-fro paths of the molecules are so 
great that they are beyond each other's attractive forces. 
The molecules, therefore, move in straight lines, until 
they either collide against one another, or against the 
side of the vessel in which they are contained. 

Gases tend to expand indefinitely, and, since their molecules are be- 
yond the range of mutual attraction, they produce a pressure against 
the walls of the vessel that contains them. 

Unlike liquids, gases contained in vessels possess no free, limiting, up- 
per surface. 

When a gas is enclosed in a bottle, it presses upwards against the 
cork, as well as against the sides and base. 

The earth' s atmosphere is densest near the surface because the attrac- 
tive force of the earth causes the upper layers of air to press with con- 
3 



34 NATURAL PHILOSOPHY. 

siderable force on the lower layers. Towards the upper limits of the 
air the atmosphere is very rare. Were it not for the attraction of the 
earth, the atmosphere would entirely leave the earth. 

When a balloon rises very high above the earth' s surface, the gas it 
contains expands, and occupies a much greater bulk than it did near 
the surface. If a balloon, at the time of its ascent, contains too much 
gas, it may burst on reaching moderately great heights, unless some 
arrangement is provided for the escape of the excess of gas. 

41. The Ultra-gaseous or Radiant State, is the state 
in which gaseous matter exists when it has been greatly 
rarefied. The number of molecules in a given space is 
then relatively so few that the molecules move through 
comparatively great distances before striking or colliding 
against each other ; in other words, their mean-free-paths 
are greatly increased. 

If a gas is rarefied to the jo o£ ottts - °f its density at atmospheric pres- 
sure, it must contain but one molecule in the space in which it formerly 
contained one million molecules. For the same length of path, there- 
fore, each molecule has but the jos^o oo chance of striking another 
molecule that it originally possessed ; or, in other words, its mean-free- 
path is increased one million fold. 

In the radiant state of matter, the mean-free-paths of 
the molecules are so great, that the molecules move in 
straight lines across the containing vessel without striking 
or colliding against one another. On striking the walls of 
such vessel, or anything in the vessel, they again fly off in 
straight lines. If the walls of the vessel or any object 
inside the vessel be heated, any molecule which collided 
against such part would fly off with additional force in 
straight lines. 

42. The Radiometer, an invention of Crookes, is an 
apparatus in which an easily rotated wheel, provided with 
vanes or arms surrounded by a gas in the ultra-gaseous 
state, is set into rapid rotation, when the opposite faces 
of the vanes are unequally heated by exposure to a source 
of light or heat. 



THE CONDITIONS OF MATTER. 



35 



In order to ensure this unequal heating of the oppo- 
site faces of the vanes, they are silvered on one side and 
covered on the other side with lamp- 
black. 

The vanes are attached to a light vertical 
axis, as shown in Fig. 5. On exposure to 
light or heat, the blackened surfaces absorb 
heat and become hot, while the silvered 
surfaces throw off the heat and remain rela- 
tively cold. The molecules of gas touching 
the heated surfaces are shot off in greater 
numbers and with greater force from the 
lamp-blacked surfaces than from the sil- 
vered surfaces. 

The reaction thus produced by the mole- 
cules flying from the lamp-blacked surfaces 
causes a rotation of the vanes in a direction 
opposite to that in which the molecules fly 
off. 

43. Influence of Heat on the 

r* ji'j. r n/r a.j. avi Fig. 5.— Crookes' Radiometer. 

Condition of Matter. — Solids are 5 

changed into liquids by the action of heat. They are then 

said to have been melted or fused. 

Some substances are easily melted or fused. Ice, for 
example, melts at quite a low temperature. Butter soft- 
ens when brought into a warm room. Other substances 
are melted or fused only by the action of intense heat. 
Cast iron requires the heat of a blast furnace to melt it. 
Substances that are difficult to melt or fuse are called 
refractory substances. 

When molten substances lose the heat which caused 
them to fuse, they again become solid. This process is 
called solidification. Thus water solidifies or freezes when 
it loses sufficient heat. Cast iron is obtained in any de- 
sired form by pouring it, when melted, into moulds, in 
which it solidifies on cooling. All liquids are changed 
into solids when they lose sufficient heat. 





CHAPTER IV. 

FORCE AND MOTION. 



o**;o« 



44. Inertia. — 



Experiment 15. — Attach a heavy weight to a string and hold it 
so that it can swing like a pendulum. Observe that an effort is re- 
quired to start it swinging ; and that, when swinging, an effort is required 
to stop it. 

In other words, on account of its inertia, the weight will neither of 
itself begin swinging, nor of itself immediately cease swinging, but re- 
quires some force to act on it. Stated more generally, a body never 
begins to move, or alters the direction or speed of its motion, unless 
some force acts on it. 

45. Force is that which is necessary to cause a body to 
begin to move, or to alter either the direction or speed of 
its motion. 

A great variety of natural forces exist. Some of the most import- 
ant of these are, 

1. The force of gravitation, which causes unsupported bodies to fall 
to the ground. 

2. The forces of molecular attraction and repulsion. 

3. The force of atomic attraction, or chemical affinity. 

4. The forces of electric and magnetic attraction and repulsion. 

5. The forces of light and heat. 

6. The vital forces that cause movements in living bodies. 

36 



FORCE AND MOTION. 37 

46. Dynamics is that branch of Natural Philosophy 
which treats of forces and their effects. 

Dynamics may be divided into, 

Statics, which treats of forces that counterbalance one 
another, and which therefore, produce no motion or 
change of motion ; and 

Kinetics, which treats of forces that do not counterbal- 
ance, and which therefore cause motion or change of mo- 
tion. 

47. Motion and Rest Relative. — Absolute rest is im- 
possible on the earth, since all things thereon are being 
carried with the earth, both as it rotates on its axis and as 
it revolves around the sun. We may, however, speak of a 
body as being at rest when it is not changing its position 
in relation to neighboring bodies. 

A person sitting in a moving train of cars is at rest as regards the car, 
since he does not change his position relatively to other objects in the 
car, although both he and the car are in rapid motion. 

The person, moreover, is breathing, the blood is moving through his 
heart, arteries, veins, and capillaries ; and the molecules in his body, 
and in the inanimate objects around him, are in rapid to-and-fro motions. 
Absolute rest, therefore, is an impossibility. 

48. The Elements of a Force. — Three things must 
be known in order to measure the effects produced by any 
force : 

1. The point of application, or the point at which the 
force acts. 

2. The direction in which the force acts. 

3. The intensity with which the force acts. 

Forces are generally represented by straight arrows ; the 
intensity of the force is represented by the length of the 
arrow ; the direction of the force, by the direction in which 
the arrow points ; and the point of application of the force 
is considered as being situated at that end of the arrow 
which is placed against the string of the bow. 

D 




38 NATURAL PHILOSOPHY. 

Thus, in Fig. 6, the body A, has its weight, or the force with which 
it is pulled downward by the attraction of the earth, represented by the 
length of the arrow g B. The direction of gravity is 
vertically downward, as indicated by the direction in 
which the arrow points, and the point of application 
of the force is indicated by the point g. 

When forces are represented by arrows, a certain por- 
tion of the length, as, for example, one inch, or one cen- 
resentation 6 ?/ timetre, is taken to represent a certain value or unit of 
Force, force. Thus, in the figure, if the arrow g B y were two 

inches, or two centimetres long, the figure might represent a force of two 
units acting at the point g, in the direction of g B. 

49. The Direction in which the Force Acts. — 

Experiment 16.— Take hold of a book and draw it toward you. Ob- 
serve that the book moves toward you. Push it ; observe that it moves 
from you. 

The direction in which a force acts determines the direc- 
tion in which the body moves. 

50. The Point of Application of the Force. — 

Experiment 17. — Place one end of a ruler against a book lying on 
a table, and push the book. Observe that the kind of motion the book 
acquires depends on the part touched by the ruler. If the ruler be placed 
near the middle of one of the edges of the book, a push will move it 
straight forward in the direction you are pushing ; but if the ruler be 
applied near a corner, although the book may still advance when pushed, 
it will, at the same time, turn partly around. 

The point at which a force is applied determines the 
nature of the motion produced. 



51. The Intensity of the Force. — 

Experiment 18. — Push the book with more force in one instance 
than in another ; observe that its motion is more rapid when the greater 
force is acting upon it. 

The intensity of a force which causes a motion, deter- 
mines the rapidity of that motion. 

52. Time is the measure of the duration of a phe- 
nomenon. 

The unit of time is a second, or the -g^lxnT P ar * °f a 






FORCE AND MOTION, 39 

mean solar day ; i. e. the mean day of the sun-dial, or the 
day represented by ordinary clocks. 

53. Velocity. — The velocity of a body is the rate at 
which it moves, and may be expressed as the distance 
through which it would move in a given time, if the rate 
were not changed. The distance is generally measured in 
feet or centimetres, and the time in seconds ; thus, by a 
velocity of six feet per second, we mean a velocity that 
will carry the body through six feet in one second of 
time. 

In order to compare velocities, some standard or unit of 
velocity is taken. This unit is either one foot per second, 
or one centimetre per second, or one mile per hour. 

The velocities in feet per second, centimetres per second, 
miles per hour, and kilometres per hour, for a number of 
objects are given below. 1 

54. Mass. — If one body is larger than another, it will 



1 Table of Velocities. 

Feet Miles 

per sec. per hr. 

Snail 2^ 0.00341 

Man swimming (Highest Kecord) . 4.022 2.74 

Military quick-step 4.5 3.07 

Man walking (Highest Eecord) . 11.985 8.17 

Man running " . . 30.61 20.87 

Man skating " . . 37.71 25.71 

Horse trotting " . . 42.93 29.27 

Horse galloping " . . 51.77 35.3 

Man bicycling " . . 52.80 36.0 

Eailroad-train " . . 165.08 112.5 

Swallow's flight 131.2 89.45 

Sound in air at 0° C 1090 743 

Eifle bullet 1330 906.6 

Pomtonequatorowingtoearth'sj 152Q im ^^ 1668 

rotation > 

Centre of earth by revolution 1 101000 &%m o mm mm 

around the sun > 



Cms. 


Kms. 


per sec. 


per hr. 


i 

8^ 


0.0055 


122.6 


4.413 


137.5 


4.94 


365.4 


13.16 


933.2 


33.60 


1150 


41.40 


1309 


47.12 


1578 


56.8 


1610 


57.96 


5030 


181.1 


4000 


144.0 


33,230 


1196 


40,550 


1460 



40 NATURAL PHILOSOPHY. 

be found that more force is required to give the larger 
body a given velocity in a given time. 

The mass of a body must not be confounded with its 
weight. The mass of a body, or the quantity of matter it 
contains, is proportional to the number of its molecules ; 
that is, if we double the number of its molecules, we 
double the mass of the body ; if we halve the number of 
its molecules, we halve the mass of the body. The mass 
of a body is the same in all latitudes, and would be the 
same at the centre of the earth as at the surface; but the 
weight of a body varies slightly with the latitude, being 
somewhat greater at the poles than at the equator, and at 
the centre of the earth a body has no weight. 

It is evident, therefore, that in all latitudes two equal 
masses will counterbalance each other in a balance. 

55. Laws of Motion.— The following laws, known 
generally as Newton's laws of motion, express the prin- 
cipal phenomena of mass motion. 

56. First Law of Motion. — A body at rest will continue 
at rest, or a body in motion will continue in motion in a straight 
line, with a uniform velocity, until acted on by some external 
force. 

. The first law of motion is a mere statement of the prop- 
erty of inertia, and is sometimes called the law of inertia. 
Since matter has no ability either to start itself moving, 
to stop moving, or to change the direction of its motion ; 
if at rest, it must continue at rest ; or, if moving, it must 
continue moving, until acted on by some external force. 

57. Second Law of Motion. — Any change in the 
direction or in the amount of motion is proportional to the 
force acting, and takes place in the direction in which the 
force acts. 

The amount and character of the motion produced by 
any force, depends on the elements of that force. The 



FORCE AND MOTION, 41 

same force acting on two masses, one twice as great as the 
other, will impart to the smaller mass a motion twice as 
great as to the larger. 

A horse can pull a light wagon much faster than it can pull a heavy 
cart. An empty wheelbarrow can be pushed much faster on a level 
than a heavily loaded wheelbarrow. A boy can run much faster when 
unimpeded than when carrying a weight on his back. 

The amount of motion of a body, therefore, depends 
not only on the quantity of matter the body contains, but 
also on the intensity of the force causing its motion. 

58. Momentum. — The momentum of a moving body is 
the amount of motion it possesses. 

The momentum of a moving body, or the quantity of 
motion it possesses, is equal to the mass of the body 
multiplied by its velocity. 

59. Examples of Momentum. — A drop of rain may scarcely bend 
the blade of grass on which it falls ; a moderately large hailstone, fall- 
ing with about the same velocity, may cut the leaves and branches from 
trees, while a rifle-bullet, from its more rapid motion, may carry death 
in its path. 

A floating chip is harmless when it strikes the sides of a small boat, 
but a floating log may crush the boat, if caught against a wharf or other 
fixed obstacle. Even a powerful ship, caught between two large ice- 
bergs moving in opposite directions, may be as completely crushed as 
is an egg shell when trodden on. 

If, while in motion, we strike our bodies against any fixed obstacle, 
as a tree, the injury received will depend on the speed with which we 
are moving. If walking at a moderate speed, the injury would prob- 
ably be but slight ; if running, we may break a bone ; if thrown from 
a carriage, or from a car while in rapid motion, we may lose life. 

60. Another Phrasing of the Second Law of Mo- 
tion. — A force produces the same effect on a body whether that 
body be moving or at rest ; whether it be the only force acting ; 
or whether other forces are also acting on the body, 

A weight dropped to the floor of a rapidly-moving car strikes the floor 
directly under the place from which it fell. The car-floor does not move 
from under the weight while it is falling, since the weight is moving for- 
ward as rapidly as the car. 



42 NATURAL PHILOSOPHY. 

A mounted acrobat at a circus, in jumping through a hoop, does not 
jump forward ; if he did he would be carried over the horse's head. 
He simply jumps up into the air, and, since his body has the same on- 
ward velocity as the horse, he falls again on the horse's back, just as 
the weight dropped to the floor of the car, strikes the floor directly un- 
der the place from which it fell. 

61. Third Law of Motion. — Action and reaction are 
equal in amount and opposite in direction. 

When a falling body strikes the earth, it imparts to the earth a mo- 
mentum equal to its own. The motion imparted to the earth, however, 
is exceedingly small as compared with that of the falling body, because 
the mass of the earth is so much greater. 

A ball, shot from a gun, produces a recoil or kick, in which the mo- 
mentum or amount of motion in the gun is equal to that of the ball and 
is opposite in direction. The mass of the gun is so much greater than 
that of the ball, that the actual velocity imparted to the gun is compar- 
atively small. 

62. Varieties of Motion. — When a body moves 
through equal distances in equal times, its motion is said 
to be uniform. 

When a body moves through unequal distances in 
equal times, its motion is said to be varied. 

If the velocity of the body changes at a uniform rate, 
we say that its motion is uniformly varied. 

When the velocity regularly increases, the motion is 
said to be uniformly accelerated. When the velocity regu- 
larly decreases, the motion is said to be uniformly retarded. 

Excluding the effect of the resistance of the air, an 
example of uniformly accelerated motion is seen in the 
case of a falling body, in which gravity is constantly 
adding uniformly to the motion which the body has 
already acquired; its motion, therefore, is uniformly ac- 
celerated. 

An example of a uniformly retarded motion is seen in 
a body thrown vertically upwards. Such a body must 
have a uniformly retarded motion, because gravity is con- 
stantly decreasing its motion uniformly. 



on- 



FORCE AND MOTION, 43 

Bodies whose motion is either uniform or varied, may- 
move in straight lines or in curves ; that is, their motion 
may be rectilinear or curvilinear. 

Rectilinear motion is that in which the body moves in 
straight lines. 

Curvilinear motion is that in which the body moves in 
curved lines. 

In rectilinear motion the body continues to move in the 
same direction. In curvilinear motion, the body is con- 
stantly changing its direction. When a body is moved 
around a fixed point, as a wheel on its axis, the motion 
is said to be rotary. 

It is evident from what has been stated concerning the first law of 
motion that a rectilinear motion does not require the constant action of 
a moving force, while a curvilinear motion can only take place by reason 
of constant action. 

63. Components and Resultants. — A body cannot 
move in more than one direction at the same time. No 
matter, therefore, how many forces may simultaneously 
act on a body, their combined action can only produce 
motion in one direction ; and this motion could have 
been produced by a single force of sufficient intensity 
acting in the proper direction. 

Any single force which will produce on a body the same 
effect as a number of separate forces, is called the resultant 
force. 

The motion produced by the action of a number of 
separate forces is called the resultant motion. 

The separate forces are called the component forces. 

64. Composition of Forces. — When several forces 
act at the same time on a body, their combined effect may 
be replaced by a single force. The method adopted for 
finding the direction and intensity of this single force is 
called the composition of forces. 

The two or more forces may act, 
1. In the same straight line. 



44 NATURAL PHILOSOPHY. 

2. At some angle with one another ; i, e. } not in the same 
straight line. 

3. In the same direction, but not in the same line ; i. e., 
parallel to one another, as a pair of horses drawing a 
wagon. 

65. Forces Acting in the same Straight Line. — 
Two cases may arise : 

1. The separate forces may act in the same direction, 
and thus aid one another. 

2. The separate forces may act in opposite directions, 
and thus oppose one another, as in the game called " the 
tug of war." 

When the forces act in the same direction, the resultant 
is equal to their sum. When two forces act in opposite 
directions the resultant is equal to their difference ; and 
in the latter case, if the two forces are of equal intensity, 
they will be in equilibrium, and the body will be at rest so 
far as their action is concerned. 

66. Parallelogram of Forces. — 

Experiment 19. — Let a pupil draw a straight line on a blackboard. 
Let another pupil draw another line in any direction, beginning at the 
point from which the first line was started, say at right angles to it. Now 
let both together hold the chalk and endeavor at the same time to draw 
the same lines as before. Observe that a line will now be drawn between 
the other two. This line is called the resultant. 

When a body is acted on by two forces in directions at 

an angle with each 
other, it will not move 
in the direction of 
either force, but in 
some direction be- 
tween them ; that is, 
the resultant will lie 
somewhere between 
the two components. 

Thus, suppose a solid body at Z>, (Fig. 7), be simulta- 




B 

Fig. 7.— Parallelogram of Forces. 



FORCE AND MOTION. 45 

neously acted on by two forces DC and DB, in the direc- 
tions indicated by the arrows, and of such intensities that 
each acting alone would in the same time move the body 
to the points C and B, respectively. Then, under the 
action of both forces the body would in this time be car- 
ried to A. 

The value and direction of the resultant DA, are de- 
termined as follows; from the point C, the line CA, is 
drawn parallel to DB, and from the point B, the line BA, 
is drawn parallel to DC. If, now, their point of intersec- 
tion A, be connected with D, by a straight line AD, this 
line will represent the resultant of the two forces DC and 
DB. 

The figure AB CD, being a four-sided figure bounded 
by parallel lines, is called a parallelogram, and this con- 
struction is generally called the parallelogram of forces. 

This method of determining the direction and intensity 
of the two forces is a particular case of the composition 
of forces before referred to. 

The parallelogram of forces affords another example of the fact al- 
ready stated, that when two or more forces simultaneously act on the 
same body, each produces the same effect as if it acted alone. Thus, by 
the force DC, the body would be carried from D, to C, or its equal from 
B, to A ; by the force DB, acting for an equal time, it would be carried 
from D, to B, or its equal, from C, to A. We see that each force has 
produced the same amount of effect as if it acted alone ; for, while the 
force DC, has carried the body through a distance equal to DC, the force 
DB, has carried it through a distance equal to A C. 

67. Parallel Forces. — When two parallel forces act in 
the same direction, their resultant is always equal to their 
sum ; but the point of application of the resultant does 
not coincide with the points of application of either of 
the two forces. 

When the two forces are of equal intensity, the resultant is situated 
midway between them ; but when they are of unequal intensity, the 
point of application of the resultant lies nearer to the stronger force. 



46 NATURAL PHILOSOPHY. 

Thus, a team of two horses abreast, tugging at the whipple-tree of a 
vehicle, produce a resultant at the centre of the whipple-tree if they 
exert equal forces. If they exert unequal forces the resultant shifts to 
the side of the stronger horse. 

68. Resolution of a Force. — By the resolution of any 
force is meant the finding of the components which will 
produce that force. This process is the reverse of that of 
the composition of forces. 

Any number of single components acting on a given point may be 
resolved into a single resultant, and any single force may be resolved 
into any number of component forces. If, however, the direction and 
magnitude of the resultant of two forces are known, and the direc- 
tion and magnitude of one of 

-™^2^ it s components are known, the 

^^^^ direction and magnitude of its 

^^^^ \ remaining component may be 

^^^ ! determined. Thus, suppose a 

certain force moves a body from 
Fig. 8.— Kesolution of Forces. 4 , ^ ,^. ox . 

5 J, to D, (Fig. 8), in a given 

time and that one of its components would in the same time move it 
from A y to B ; to find the direction and magnitude of its other compo- 
nent, complete the parallelogram ABDC, and A (7, will represent the 
direction and intensity of its other component. 

69. Centrifugal Force. — The inertia of a moving 
body, if unchecked, will cause the body to continue 
moving in a straight line forever. To stop its motion, or 
to change the direction of its motion, some other force 
must act on it. 

A stone tied to a string and whirled around, will continue moving in 
a circular path as long as the string is held in the hand ; but if we let 
the string go, the stone will no longer move in a circle, but will fly off 
in a straight line, in the same direction as that in which the stone was 
moving at the time the hand released the string. 

The string is constantly keeping the stone at a fixed distance from the 
hand, and preventing it from moving away from the hand. Since, how- 
ever, the stone neither moves towards the hand nor away from it, these 
two forces must be equal to each other ; and since they are directly oppo- 
site, they neutralize each other, and the body retains its circular path. 



FORCE AND MOTION. 47 

The force exerted in a direction outwards from the centre, 
by a body moving in a circular path, is called the centrifugal 
force. The force which is exerted from without towards 
the centre is called the centripetal force. If the centripetal 
force ceases, the body will move in a straight line ; and at 
the same time the centrifugal force will cease, since it is a 
consequence of the rotation. 

The motion of the earth around the sun affords a good instance of 
the so-called centrifugal and centripetal forces. In consequence of the 
motion originally given it, the earth is constantly tending to move away 
from the sun. The sun, however, is constantly attracting the earth ; and 
these two causes make the earth move in an almost circular path around 
the sun. 

70. Laws of Centrifugal Force. — The laws of cen- 
trifugal force, considered in relation to a small body rotat- 
ing uniformly about a fixed centre, are as follows : 

1. The centrifugal force is proportional to the mass of 
the rotating body. 

2. The centrifugal force is proportional to the square of 
the velocity of the rotating body. 

If the mass of the body be doubled, twice the amount 
of force will be required to keep it from moving away 
from the centre of motion. If the velocity of the body 
be doubled, four times the force will be required to keep 
it from moving away from the centre of motion. 

71. Examples of Centrifugal Force. — Drops of mud 
thrown by centrifugal force from the wheels of a carriage 
in rapid motion, fly off in straight lines. Grindstones and 
flywheels of engines, when in very rapid rotation, are some- 
times burst by the action of centrifugal force. The tend- 
ency of the different portions of the wheel to continue 
moving in the direction in which they are moving at any 
given moment, becomes, eventually, stronger than the co- 
hesion of the particles, and the stone or wheel flies into a 
number of pieces, which move with considerable velocity 
in different directions. 



48 NATURAL PHILOSOPHY. 

The shape of the earth is not that of a perfect sphere. The equa- 
torial diameter, or the distance through the centre at the equator, is 
somewhat greater (about one-third of one per cent.) than the polar 
diameter, or the distance through the centre at the poles. This bulg- 
ing of the earth at the equator was caused by the action of centrifugal 
force. 

Problems. 

1. The distance between the Pennsylvania stations at Jersey 
City and Philadelphia is 89.6 miles. The Limited Express runs 
the distance in 1 hour and 59 minutes. Assuming its speed to be 
uniform between these points, what would be its velocity in miles 
per hour. Arts. 45.176 miles per hour. 

2. What would be the velocity of the above train if it made 
the run between the two cities in one hour and thirty minutes ? 

Arts. 59.733 miles per hour. 

3. The velocity of light is 186,414 miles per second. What is 
its velocity in kilometres per second? 

Ans. 300,000 kilometres per second. 

4. How long would it take a carrier pigeon to fly between New 
York and Philadelphia (89.6 miles), assuming its velocity to be 78 
miles per hour? Ans. 68.9 minutes (approximately). 

5. What is the momentum of a 50-pound hammer moving at a 
velocity of 1 J feet per second ? Ans. 75 lbs.-ft.-per-second. 

6. A mortar discharges a 300-lb. projectile with a velocity of 
800 feet per second. What is its momentum at this velocity in 
lbs.-ft.-per-second. Ans. 240,000 lbs.-ft.-per-second. 

7. A man weighing 150 lbs. rides a bicycle weighing 25 lbs. at 
a speed of 20 miles per hour. What is the momentum of the man 
and bicycle together, in lbs.-ft.-per-second ? 

Ans. 5133 lbs.-ft.-per-second. 




CHAPTER V. 

GRAVITATION. 



72. Gravity.— Unsupported bodies fall to the earth be- 
cause they are attracted towards it by a force called the 
force of gravity ■, which is the attractive force one mass of 
matter exerts upon another. 

The real nature of gravity is not thoroughly understood, but, from 
repeated observation and experiment, every particle of matter in the 
universe acts as though it attracted every other particle of matter, and 
it is believed that this attractive force would eventually bring all matter 
to one place, were it not for opposing causes. 

It is certain that the earth attracts the moon, but how it does so 
across absolutely empty space is not easy to understand. Although 
gravity apparently acts at a distance^ yet the fact that the universal 
ether, a highly tenuous medium, always occupies and fills even what are 
ordinarily called empty spaces, has led to the belief that the phenomena 
of gravitation are essentially connected with this medium. 

73. Weight. — The weight of a body is due to the action 
of gravity on the matter the body contains. A quart of 
water has twice the weight of a pint, because it contains 
twice as much matter for gravity to act upon. 

A body placed on any support exerts a pressure on such 
support proportional to its weight. 

This pressure is due to the attraction between the earth 
and the body. 

74. Density. — If different kinds of matter such as an 

4 49 



50 NATURAL PHILOSOPHY. 

apple, a block of wood, or a piece of iron be cut into 
blocks of the same size, it will be found that these blocks 
have different weights. Since the weight of a body is due 
to the action of gravity on the matter it contains, it is evi- 
dent that as indicated by their weights, different volumes 
of different substances contain different quantities of 
matter. 

By the density of a substance is meant the mass or 
quantity of matter contained in a unit volume of that 
substance as indicated by its weight. It is evident, there- 
fore, that equal volumes of different kinds of matter con- 
tain different masses or different quantities of matter. 
The denser a substance is, the greater the quantity of 
matter it contains in unit volume. 

Thus, the density of sugar is the mass or quantity of 
matter contained in one cubic centimetre of sugar. The 
density of lead is greater than the density of sugar, and 
the attraction of the earth on a cubic centimetre of lead 
is greater than the attraction of the earth on a cubic cen- 
timetre of sugar; i. e. y the lead weighs more per unit 
volume. 

75. English and French Systems of Weight. — The 

unit of weight, both in the United States and in England, 
is the pound. Unfortunately, the pound is of two distinct 
kinds ; viz., the pound avoirdupois and the pound troy. The 
one seven-thousandth part of a pound avoirdupois or the 
five thousand seven hundred and sixtieth part of a pound 
troy is called a grain. Although the grains are the same 
in both pounds, their other subdivisions are different ; in 
the pound avoirdupois there are 16 ounces ; in the pound 
troy, 12 ounces. 

In France and throughout Europe generally, the unit 
of weight is the gramme. This unit has various deci- 
mal multiples and submultiples. The gramme is the 
weight of a cubic centimetre of water at the temperature 



GRAVITATION. 



51 



of its greatest density ; viz., at 39.2° Fahr., or 4° C. The 
gramme is equal to about 15.432 English grains. The 
names and values of the various multiples and subdivi- 
sions of the gramme are given below. 1 

76. Law of Universal Gravitation. — The law of uni- 
versal gravitation was discovered by Sir Isaac Newton, an 
English philosopher. It may be stated as follows : 

The attraction betiveen any tivo particles of matter in the 
universe is directly proportional to the product of their masses, 
and inversely proportional to the square of their distances apart. 

One thing is said to be directly proportional to another when it increases 
in the same ratio that the other increases. If the mass of one body be 
2, and that of another be 3, the attraction between them, being directly 
proportional to the products of their masses, would be 6. If the masses 
be 4 and 6, the attraction will be 24, or four times as great as in the case 
of the two bodies first referred to. 

One thing is said to be inversely proportional to another when it in- 
creases in the same ratio that the other decreases. Thus, if one is 
made twice as great, the other becomes half as great. If at a certain 
distance, the attraction between two bodies is represented by 8, then if 
this distance be made twice as great, the attraction would be but 2; 
viz., inversely as the square of the distance. 

77. Attraction Proportional to the Product of the 
Masses. — Since the force of attraction between two masses 
is directly proportional to the product of the masses, doub- 
ling the mass of one of the two bodies doubles the attrac- 
tion, while doubling the mass of both bodies quadruples 



the attraction. 








1 Multiples and Subdivisions of the Gramme. 








grains. oz. avoir, lbs. avoird. 


1 Kilogramme = 


1000 


= 


15432.34 35.274 2.2046 


1 Hectogramme = 


100 


= 


1543.23 3.5274 0.22046 


1 Decagramme = 


10 


= 


154.32 0.35274 


1 Gramme = 


1 


= 


15.43 0.035274 


1 Decigramme = 


0.1 


= 


1.543 


1 Centigramme = 


0.01 


= 


.154 


1 Milligramme = 


0.001 


= 


.0154 



52 NATURAL PHILOSOPHY. 

A man who can jump six feet high on the surface of the earth, if 
transferred to the surface of the moon could jump thirty-six feet high, 
owing to the lesser attraction of the moon upon his body, while on the 
sun he could jump only two and one-half inches high, owing to the 
greater attraction of the sun. 

78. Attraction Inversely Proportional to the Square 
of the Distance. — Doubling the distance between two 
bodies decreases the attractive force between them to one- 
fourth its former value; halving the distance between 
them, increases its force to four times its former value. 

The farther a body is carried above the earth's surface, the less the 
attraction which the earth has for it, and the less its weight. A body 
on the earth's surface is approximately four thousand miles from the 
earth's centre. If a pound weight could be carried four thousand miles 
above the earth's surface, it would weigh but one-quarter of a pound, 
since, its distance from the earth's centre being doubled, the earth's at- 
traction for it is diminished to one-fourth. 

Since the earth is bulged out at the equator, a body at the equator is 
farther from the earth's centre than at the poles. The same body, there- 
fore, would weigh more at the poles than at the equator ; a man weigh- 
ing 194 pounds at the equator would weigh 195 pounds at the poles. 

If, however, we take a body below the surface of the earth, it would 
weigh less than at the surface, since the parts of the earth that are 
above it, would pull in the opposite direction to the parts of the earth 
below it, and would, therefore, decrease its weight. At the centre of 
the earth, a body would have no weight, since the attraction would be 
the same in all directions. 

The combined effect of mass and distance on the amount of attraction, 
is seen in the tides of the ocean, which are caused by the attractions of 
the sun and moon. The mass of the sun is much greater than that of 
the moon, but since the moon is so much nearer the earth than the sun, 
the influence which the moon exerts in causing tides is much greater 
than that exerted by the sun. 

In order to understand the effects of gravity, we must 
ascertain, as in the case of other forces, 
First The direction in which it acts. 
Second. Its point of application. 
Third. Its intensity. 



GRAVITATION. 



53 




W 



Fig. 9 —The Plumb-Line. 



79. The Direction of Gravity. — Gravity acts in a 
vertical direction or approximately 
towards the earth's centre. A ver- 
tical line is perpendicular to a sur- 
face of water at rest. 

The direction of gravity may be as- 
certained by the use of the plumb- 
line, which consists of a weight W, 
Fig. 9, attached to the end of a 
string. If the other end of the string 
be held in the hand, when the weight 
has come to rest the string will be 
stretched in a vertical direction, and 
the plumb-line will point approxi- 
mately towards the earth's centre. 

80. The Point of Application.— -Centre of Gravity. 
— As gravity acts alike on all molecules in a body, there 
must be as many separate points of application as there 
are separate molecules. 

The separate pulls, which may be regarded as so many 
separate components, may be replaced by a single result- 
ant, equal to their sum, because they all act in the same 
direction; viz., vertically downward. This resultant pull 
is equal to the weight of the body, and its point of appli- 
cation is called the centre of gravity, 
because it is a point at which the 
whole weight of the body may be re- 
garded as collected. 

In Fig. 10, the vertical dotted lines 
a, 6, c, d, e, f, etc., represent the sepa- 
rate pulls which gravity exerts on the 
molecules of the body. GA, repre- 
sents their resultant, and G, the point 
of application of this resultant, is called 
the centre of gravity of the body. 

The centre of gravity of a body is independent of the position in 
which it is held and whether the body is at rest or in motion. 




Fig. 10 -The Centre of 
Gravity. 



54 



NATURAL PHILOSOPHY. 



81. Method of Determining the Centre of Grav- 
ity. — Suspend any body, such as a chair, by a string 
attached to any part, such as the top or the back, and 
allow the chair to come to rest. Observe the direction 
in which the string, if extended downwards, would pass 
through the chair. The centre of gravity will be situated 
somewhere in this line, which is called the line of direc- 
tion of gravity. Attach the string to some other part of 
the chair, such as one of the rungs ; again suspend it, and 
observe, as before, the direction of the line extended down- 
wards along the string when the chair is at rest. The centre 
of gravity of the chair will be situated somewhere in this 
line. The centre of gravity is a point, and a point in order 
to be situated in each of two different lines, must be at their 
intersection. The point, therefore, where these two lines 
intersect each other will be the centre of gravity of the chair. 



Experiment 20. — Bore small holes at a, b, and c, in a rectangular 
plate of tin as shown in Fig. 11. Tie a 
string to the plate at b, and suspend the 
plate hy the string, and, when it has 
come to rest, draw the line b d, in the 
direction of the string extended. Then 
attach the string to some other point, as c, 





e d f e 

Fig. 11 —Method of Finding the Centre of Gravity, 

and, proceeding as before, draw the line c e. The centre of gravity of 
the plate will be found at g, where the line b d, is cut by the line c e. 

82. A Body Supported at its Centre of Gravity 



GRAVITATION. 55 

must be at Rest. — When in Fig. 11, the plate of tin 
comes to rest in the position shown at the left, the shaded 
portion b cfd, must be of the same weight as the unshaded 
portion, ab de; for, were either of these portions heavier 
than the other, it would fall, and the line d 6, would take 
some other direction. So also the shaded portion c e a, is 
of the same weight as the unshaded portion c ef. The 
same is true of any other position in which the body 
comes to rest when suspended ; the part of the body on 
one side of the line of direction is always equal in weight to 
that on the opposite side. A body at rest remains at rest 
when supported at its centre of gravity, because its weight 
is then equally distributed about its point of support. 

83. Equilibrium of Bodies Supported on an Axis. 

— A body supported on a horizontal axis, around which it 
is free to turn, will be in equilibrium, only when its point of 
support and its centre of gravity are in the same vertical line. 
The point of support, in such cases, may have three dif- 
ferent positions : 

1. Above the centre of gravity. 

2. Below the centre of gravity. 

3. At the centre of gravity. 

These three positions correspond to three different kinds 
of equilibrium ; viz., stable, unstable, and neutral equilibrium. 

84. Stable Equilibrium about an Axis. — Here the 
point of support is above the centre of gravity, and the 
body, when left to itself, again assumes a position of 
stable equilibrium. 

Experi ment 21 .—Cut a disc from a flat piece of cardboard and make 

a hole in it at 8, with a needle, so as to allow 

the card to move freely around the needle. ^^T^^^^^^Mr 

Hold the needle horizontally as shown in ^ ^&mjSm^ aJSNEL 

Fig. 12. Observe that the card comes to rest f^^\ 1\ ' l- ^ <<iP ^^J / 

in a position of stable equilibrium. Here the [ »g ) 

point of supports, is above the centre of grav- V / 

ity G, and in the same vertical line with it „,^ s ~^ ,, ,, .,., . 
,g G , Fig.12— Stable Equilibrium. 



56 



NATURAL PHILOSOPHY. 



85. Unstable Equilibrium about an Axis. — Here 
the point of support is directly below the centre of grav- 
ity. Any motion of the body causes the centre of gravity 
to fall, and the body to assume a position of stable equi- 
librium. 



Experiment 22. 




Fig. 13.— Unstable Equilib- 
rium. 



Hold the pasteboard disc as shown in Fig. 13. 
Observe that it will be in a position of un- 
stable equilibrium. Here the point of sup- 
port S, is directly below the centre of grav- 
ity, G, and is in the same vertical line with 
it. If the disc be slightly moved, the centre 
of gravity falls, and the disc assumes the posi- 
tion of stable equilibrium shown in Fig. 12. 



86. Neutral Equilibrium about an Axis. — Here the 
point of support coincides with the centre of gravity, and 
the body will remain at rest into whatever position it may 
be moved about the axis. 




Experiment 23.— Hold the pasteboard disc as in Fig. 14. Observe 
that it will come to rest in a position of neu- 
tral equilibrium, and that no matter in what 
position the disc be set, it will remain at rest. 

Here the point of support remains at the 
centre of gravity, no matter how the disc may 

be turned ' Pig. 14.-Neutral Equilib- 

87. Equilibrium of Bodies rium ' 

Resting on a Flat Surface.— When a body has more 
than one point of support, as when some portion of the 
body is resting on a flat surface, it is not necessary that 
the centre of gravity be above any one of these points of 
support, in order that the body may be in equilibrium. 
It is sufficient if the vertical line passing through the 
centre of gravity, or the line of direction, falls within the 
base on which the body rests. 

When the centre of gravity is as low as it can get, the 
body is in stable equilibrium. The lower the centre of 
gravity, and the greater the area of the base on which the 
body rests, the more stable the equilibrium. When the 
relative positions of the centre of gravity and the point 



GRAVITATION. 



57 



of support remain the same in any position of a body, 
the body is in neutral equilibrium. 

A book placed as at A, Fig. 15, will be in stable equilib- 





Fig. 15.— Stable Equilibrium. 

rium, since it is resting on a large base, and its centre c: 
gravity is as low as it can get. 

In order to overturn the book from this position, its 
centre of gravity must be raised until the vertical passing 
through it falls outside the base. 

When standing as at J5, Fig. 16, the book will still be in 
stable equilibrium ; but since the base on which it rests is 
smaller than when placed as at A, 
its centre of gravity is higher, and 
the equilibrium is less stable than at 
A ; i. e. a slight push will bring the 
centre of gravity over the base and 
overturn it. 

When placed as at 0, Fig. 17, the 
equilibrium, though still stable, will 
be less stable than at 2?, since the base on which the 
book rests is still smaller, and the centre 
of gravity higher. 

A sphere, resting on a level table, is in 
neutral equilibrium, because no movement 
can change the relative positions of its cen- 
tre of gravity and its point of support ; the 
centre of gravity being at the centre of the 
sphere, and the point of support immedi- 
ately beneath. 

In a boat loaded with people, the equi- 
librium is more stable if the passengers 
remain seated, than if they stand up, because, when they 



Fig. 16 —Stable Equilib- 
rium, but less Stable 
than at A. 




Fig. 17. — Stable 
Equilibrium, but 
less Stable than 
atB. 



58 



NATURAL PHILOSOPHY. 




Fig, 18.— Experiment 
in Stable Equilib- 
rium. 



stand up, the centre of gravity is raised, and the boat, if 
small, may upset. 

Experiment 24. — Fasten a stout pin, a, upright in a cork, d, placed 
in the mouth of a narrow bottle, c, Fig. 18. Stick the blunt end of a 
stout needle e, in the cork, on the sides of which two 
penknives / and g are placed as shown. Carefully 
place the point of the needle on the head of the pin, 
and observe that it will not only rest there in a posi- 
tion of moderately stable equilibrium, but that the 
cork and knives may even be moved around without 
falling. As the head of the pin is generally more or 
less rounded, it should be rubbed flat with a file. 

The centre of gravity may 
be situated outside a body, 
as in the case of a ring, 
where the centre of gravity 
is at the centre of the ring. 

88. The Laws of Falling Bodies.— The 

laws of falling bodies were discovered by 
Galileo, an Italian philosopher. They may 
be expressed briefly as follows : 

1. First Law. — The velocity of a falling body 
is independent of its mass. 

Gravity acts on each molecule of the 
body; if the molecules were all separated, 
each would fall to the earth with the same 
velocity, because the same force acts on each. 
Their being united in one mass makes no 
difference, since gravity acts on each mole- 
cule as though it were alone. The number 
of molecules in any body, or in its mass, 
therefore, has no effect on its velocity. 

Should we yoke together two equally fast horses 
abreast, so as to give them perfect freedom of motion, 
the two together would not be able to run any faster 
than either separately. It is the same with the motion of molecules 
toward the earth, 



Fig, 19 — Bod- 
ies Falling 
through an 
Empty Space. 



GRAVITATION. 59 

2. Second Law. — The velocity of a falling body is indepen- 
dent of the shape or nature of the body. 

So far as our every-day experience goes, this law would 
appear to be incorrect, since a piece of gold in the shape 
of a ball, will fall more rapidly through the air than when 
beaten out into gold leaf; again, a small piece of cork falls 
less rapidly through the air than a piece of iron of the 
same size. 

It is the resistance of the air which causes* these appa- 
rent exceptions to the law. In a vacuum or empty space, 
all bodies, whatever their size, shape, or material, fall with 
the same velocity ; a feather and a leaden bullet, for ex- 
ample, let fall from the same height, at the same time, 
would reach the bottom of the empty or exhausted vessel 
B, Fig. 19, at the same instant. 

Experiment 25.— Let two iron weights, one weighing, say, an 
ounce, and the other weighing a pound, fall from the hand at the same 
time. Observe that the eye is unable to detect any difference in the time 
of falling. 

3. Third Law. — The velocity acquired, at the end of any 
given time, by a body falling freely from a state of rest is pro- 
portional to the time during which it has been falling. 

Thus, in a body falling freely from a state of rest, in the latitude of 
Washington, D. C, the velocity at the end of the first second is equal 
to about 32.16 feet per second, or 980.1 cms. per second. 

The velocity at the end of the second second is 32. 1 6 x 2 = 64. 32 feet 
per second. The velocity at the end of the third second is 32.16 x 3 
= 96. 48 feet per second, and so on. Here the velocity increases as the 
time and is proportional to the numbers 1, 2, 3, etc. The quantity 
980.1 cms. per second is called the acceleration of gravity. This accel- 
eration varies at different parts of the earth's surface, being least at 
the equator, where it is 978.1, and increasing with the latitude to a 
maximum at the pole, where it is supposed to be 983.1. 

4. Fourth Law. — The distances fallen through in successive 
seconds increase as the odd numbers, 1, 3, 5, 7, etc. 



60 



NATURAL PHILOSOPHY, 



A body falling freely from a state of rest passes through 16.08 feet 
during the first second of its descent. But the velocity of any falling 
body is constantly increasing, since gravity is constantly imparting an 
impulse to the body, which is added to the velocity already acquired. 

During the second second, it falls through three times 16.08 ft. or 
48.24 ft. ; during the third second, it passes through five times 16.08 ft. 
or 80.40 ft, etc. 

5. Fifth Law. — The total distance in feet through which a 
body will have fallen freely in a given time is proportional to 
the square of "the time, and is equal to the square of the time in 
seconds multiplied by 16.08. 

Thus, a falling body falls four times as far in two seconds as in one 
second, and nine times as far in three seconds as in one second. 

During the first second the body falls through 16.08 ft. ; during the 
second second it falls through 48. 24 ft. ; at the end of the second second 
it has fallen through a total distance of 48.24 + 16.08 = 64.32 ft. But 
64.32 is four times as great as 16.08; that is, at the end of the second 
second the body has fallen through a space 2 x 2, or 2 squared, greater 
than what it fell during the first second, or, in other words, the whole 
space fallen through is proportional to the square of the time. 

The actual values for the latitude of Washington, D. C, 
are given below. 1 

89. Atwood's Machine. — The velocity acquired by a 
falling body is too great to permit the direct experimental 
verification of the 3d, 4th, and 5th laws, even if the re- 
sistance of the air did not interfere with the result. Va- 
rious apparatus has, therefore, been constructed to permit 
such experimental verification. Atwood's machine and 
Galileo's inclined plane are examples of such apparatus. 



Number of 
seconds. 



Distances fallen through dur- 
ing particular seconds. 



Total distances fallen through at 
the end of any number of seconds. 



1 
2 
3 
4 
5 
6 



16.08 feet. 

48.24 " 

80.40 " 

112.56 " 

144.72 " 

176.88 " 



490.04 cms. 
1470.12 " 
2450.20 " 
3430.28 " 
4410.36 " 
5390.44 " 



16.08 feet. 
64.32 " 
144.72 " 

257.28 " 
402.00 " 
518.88 " 



490.04 cms. 
1960.16 
4410.36 
7840.64 
1225.01 
1764.14 



GRAVITATION. 



61 



In Atwood's machine, Fig. 20, the velocity of the fall is decreased 
by causing the body during its fall to raise a weight, and thus decrease 
the speed of its descent sufficiently to permit 
its fall to be followed by the eye. 

90. Galileo's Inclined Plane. — A 
body rolling down an inclined plane, 
although it moves with a uniformly 
accelerated velocity like a falling body, 
yet moves less rapidly. Galileo adopt- 
ed this device for observing the rate 
of fall. He caused a heavy ball to 
roll down an inclined plane, the 
length of which was so proportioned 
to its height, as to permit the motion 
of the ball to be readily followed by 
the eye. 

91. Projectiles. — Projectiles are 
bodies thrown through the air. They 
are acted on 

(1). By a momentary force which 
gives the projectile a uniform velo- 

•i Fig. 20.— Atwood's Machine. 

(2). By the constant force of gravity which gives it a 
constantly accelerated velocity. 
(3). By the resistance of the air. 

A projectile thrown vertically upwards must move with a constantly 
retarded velocity, since gravity is constantly acting upon it. Eventually, 
the projectile stops moving upwards and begins to descend. Disregarding 
the resistance of the air, the projectile, at any point in its descent, will 
have the same velocity it had at that point in its ascent, and will reach 
the point from which it was thrown with the velocity it had when it 
began to rise. 

When projected vertically upwards, the path of a pro- 
jectile is a straight line ; in any other direction its path 
is a curve. 




62 



NATURAL PHILOSOPHY. 



Suppose, for example, a projectile be thrown in a horizontal direction 
from F to H, Fig. 21, with a velocity that would carry it through the 
j? a ft c $ ft equal spaces Fa, ab, be, cd y and dH, during the 
1st, 2d, 3d, 4th, and 5th seconds. Gravity is 
constantly acting, and during these five seconds 
the body would fall through the spaces 1, 3, 5, 7, 
and 9 respectively. By the constant action of 
gravity on the projectile' s motion, the body would 
be at A , B, (7, 7), and E, at the end of 1, 2, 3, 4, 
and 5 seconds respectively, and would therefore 
move through the curved path, F A B C D E. 

92. Range. — A body projected hori- 
zontally strikes the ground at a hori- 
j£ zontal distance from its starting point, 
Fig, 21 -Parabolic Path which, disregarding the resistance of 
of Projectile, foe air, is equal to the distance the pro- 

jectile force would carry it during the time it was falling. 
This horizontal distance is called the range. Thus, in Fig. 
21, the body projected horizontally at F, toward H, strikes 
the ground at E ; the distance Q E, is, therefore, its range. 
If the body be projected upwards in any other direc- 
tion than vertically, its horizontal range will be twice as 

D E F G f 



1 






G 












K\ 




^ 




F 


\ 



A \ 2 3 456G 

Fig. 22.— Range of Projectile, 

great as if it had been projected horizontally, with the 
same initial velocity, disregarding the resistance of the air. 
Suppose, for example, a body be projected from A towards B, Fig. 22, 
with a velocity that would cause it to rise for three seconds ; then at the 
end of the first, second, and third seconds it would be at B, C, and D 
respectively. At D, it would reach its highest point and begin to de- 



GRAVITATION. 



63 




Fig. 23,- 



D 

-Ballistic Curve. 



scend, reaching E, F y and G, at the end of the 4th, 5th, and 6th sec- 
onds respectively. Here the range A G, would be twice as great as if 
it had been horizontally projected from D, towards G / , with the same 
initial velocity. 

93. Ballistic Curve. — Were there no' resistance offered 

by the air to a projectile, its path 
would be the curve shown in Figs. 
21 and 22, which curve is called a 
parabola. But, in consequence of 
this resistance its actual path through 
the air is in a very different curve 
called a ballistic curve (Fig. 23). 

Instead of taking the path of the 
parabola, A EB, the projectile takes 
the ballistic curve A CD. The vertical distance attained 
by the projectile, as well as its horizontal range, is dimin- 
ished by the resistance of the air. 

For this reason, the actual range of any projectile, fired from a gun, 
is much shorter than its range calculated as in Section 92 for unretarded 
velocity. 

94. The Pendulum.— A pendulum consists of a mass, 
b, Fig. 24, suspended by a string or rod a 6, from a fixed 
support a, about which it is free to move. 
The mass 6, is called the bob of the pen- 
dulum. When the pendulum is at rest, 
the bob and its supporting string assume 
the position of the vertical ab. If, now, 
the bob be raised, so as to assume the 
position shown at a c, it will, when al- 
lowed to fall, move towards its old posi- 
tion a &, along the curved line c b. When, 
however, the position a b ) is reached, the 
pendulum does not cease moving ; for, the 
momentum it has acquired in falling from 
c to 6, carries it past this position to d. 
When the pendulum reaches d, it again 
falls towards 6, and acquires momentum 




Fig. 24,-The Pendu- 
lum. 



64 NATURAL PHILOSOPHY. 

sufficient to carry it to c, and so on, continuing to swing 
to-and-fro between c and d. Each complete swing from c 
to d, or from d to c, is called a vibration or oscillation. The 
time it takes the pendulum to move through each com- 
plete swing is called the time or duration of an oscillation. 
The curved line be, or b d, which marks the distance the 
pendulum has been moved from the vertical a b, is called 
the amplitude of the oscillation. 

95. The Laws of the Pendulum. — First Law. In the 
same pendulum, if the amplitude of the oscillation is small, the 
time of oscillation for different amplitudes is nearly the same. 

Vibrations that are performed in equal times are called 
isochronous. This law is sometimes called the law of iso- 
chronism of the pendulum. 

Galileo first discovered this law by watching the motions of a lamp 
swinging at the end of a long chain suspended from the cathedral roof 
at Pisa. 

Unless the pendulum is connected with a spring or weight, the resist- 
ance which the air offers to its movement will cause it to swing through 
smaller and smaller arcs until it finally comes to rest. 

Second Law. In pendulums of different lengths, the duration 
of an oscillation is directly proportional to the square roots of 
the lengths. 

Experiment 26. — Attach a plumb bob to a short string of a given 
length, and count the number of oscillations it makes in a given time. 
Attach another plumb bob to a string nine times as long as the first : it 
will complete but one oscillation in the time the other completes three 
oscillations. Since the lengths of the two pendulums are as 1 is to 9 and 
their oscillations are as 1 is to 3, it is evident that in pendulums of differ- 
ent lengths, the duration of their oscillations is directly proportional as 
the square root of their length. 

In the latitude of Washington, a pendulum to beat 
seconds must be about 39.1 inches in length. 

96. The Intensity of Gravity. — The intensity of the 
force with which gravity acts at any place, on any given 
mass of matter, may be ascertained by the weight of that 



GRAVITATION. 65 

mass. This, however, varies in different latitudes, being 
greater at the poles than at the equator. A man weighing 
194 lbs. at the equator, would weigh 195 lbs. at the north 
or south pole. 

The number of oscillations made by a pendulum in a 
given time is proportional to the square root of the inten- 
sity of gravitation. Consequently, if we could shift a 
pendulum to some planet where gravity was four times 
stronger, the pendulum would oscillate twice as fast. 

Since gravity is the cause of the motion of the pendulum, we can de- 
termine the variations in the intensity of gravity at different parts of the 
earth, by counting the number of oscillations the pendulum makes in a 
given time. If we carried the same pendulum from the equator toward 
the pole, we should find that the number of its oscillations would in- 
crease gradually, thus showing that the force of gravity was becoming 
greater and greater. 

97. Variations in the Force of Gravity. — The force 
of gravity varies at different parts of the earth's surface: 

1. On account of the shape of the earth, which is ap- 
proximately an oblate spheroid. 

A place on the earth' s surface at the equator being at a greater dis- 
tance from the earth' s centre than a place on the surface at the poles, 
the intensity of gravity will be less at the equator than at the poles. 

2. On account of the earth's rotation on its axis. 

The centrifugal force arising from the earth' s rotation is greatest at 
the equator and nothing at the poles. Therefore, the apparent force of 
gravity varies with the latitude. 

Consequently, if the earth were at rest and were a uni- 
form spherical globe, gravity would have uniform inten- 
sity all over its surface. 



66 natural philosophy. 

Problems. 

«K>>©<00 

1. A man weighs 150 lbs. avoirdupois. Express his weight in 
kilogrammes. Ans. 68.03 kilogrammes,, 

2. What is the weight, expressed in grammes, of 200 cubic cen- 
timetres of distilled water at the temperature of its maximum 
density (4° C.) ? Ans. 200 grammes. 

3. If a boy weighs 80 lbs. avoirdupois upon a spring balance 
at the equator, what would be his weight, with the same spring 
balance, if he could be weighed at the north or the south pole ? 

Ans. 80.41 lbs. 

4. Assuming the earth to be a sphere 4000 miles in radius, what 
would the boy weigh by the spring balance at an elevation of 100 
miles above the level of the sea? Ans. 76.14 lbs. 

5. The heaviest cannons yet made weigh 110} long tons (2240 
lbs.), and are capable of throwing a projectile weighing 2000 lbs. 
Express these weights in kilogrammes. 

Ans. 112,274 kilos ; 907.2 kilos. 

6. A stone dropped into a well from the surface of the ground, 
strikes the water in the well three seconds after being released. 
What is the depth of the water in the well in feet? 

Ans. 144.72 ft. 

7. In the last example, what will be the velocity of the body 
when it strikes the water, in feet per second. 

Ans. 128.64 feet per sec. 




CHAPTER VI. 

COHESION AND ADHESION, AND PROPERTIES 
PECULIAR TO SOLIDS. 



oXKo 

98. The Force of Molecular Attraction is the force 
by which molecules either of the same or of different kinds 
of substances are held together. 

It is convenient to speak of the molecules as being held together by 
the force of molecular attraction. By this expression is meant the fact 
that they are held or constrained by the force of attraction to maintain 
a certain average distance apart during their to-and-fro movements. 

The cause of molecular attraction is unknown. Molec- 
ular repulsion, which prevents the molecules from com- 
ing together, appears to be due to heat energy. 

Cohesion is the name given to the force of molecular at- 
traction when it holds together molecules of the same 
kind of substance. Adhesion is the name given to this 
force when it holds together molecules of different kinds 
of substances. 

99. Cohesion varies greatly in different substances ; 
in some, such as iron or steel, it is very great ; in others, 
such as butter or putty, it is quite feeble. It is the cohe- 
sion of a solid that causes it to retain its shape. 

The force of cohesive attraction appears to act only at 
very small distances. If we overcome the cohesion be- 
tween the molecules of a piece of iron or china, we can- 

67 



68 



NATURAL PHILOSOPHY. 



not cause their molecular attraction again to bind them, 
by merely pressing the broken edges together. It would 
appear as if we could not thus bring a sufficient number 
of the molecules sufficiently near to one another. 

In the process of welding metallic substances, the ends that are to be 
connected in the welded joint are brought to a heat sufficient to soften 
them and are thou pressed or hammered, thus causing them to cohere 
strongly together. In electric welding, the welding temperature is ob- 
tained by passing a strong electric current through the pieces of metal 
that are to be joined. 

Dry, powdered graphite, when thoroughly cleansed, may by great 
pressure, be consolidated into a coherent mass, that may readily be cut 
into strips for use as lead pencils. 

Two fresh surfaces of lead may be made to adhere with considerable 
force, by merely pressing them together. Two clean plates of polished 
glass, such as is used for mirrors, will often cohere so strongly, when 
laid on each other, as to make it impossible to separate them without 
fracture. 

Experiment 27.— Cast a cylinder of lead about one inch in length 
and a quarter of an inch in diameter. This can be done by boring a hole 
of the proper size in a piece of hard, dry wood, 
and pouring molten lead into the hole. This 
is a dangerous operation if the wood is damp, 
as an explosive scattering of lead may occur. 
Cut the cylinder in half by resting a sharp 
knife against its side and striking the knife 
a few blows with a hammer. Attach strings 
or wires to the ends of the pieces as shown in 
Fig. 25. Press the freshly cut surfaces firmly 
together, being careful not to touch them ; ob- 
serve that they will cohere with sufficient force 
to sustain a heavy weight placed below, on a 
pan made by tying strings to the four corners 
of a piece of stout cardboard. 

100. Cohesion of Liquids. — The 

molecules of liquid substances move 
over one another so easily that we 
might suppose they possessed no cohesion. They do, 
however, exert a cohesive attraction for one another, 
though this attraction is much less than in solids. 




Fig. 25,-The Cohesion 
of Lead, 



COHESION AND ADHESION 69 

Had liquids no cohesion, the drops of dew on foliage would be flat- 
tened by gravity into thin layers, instead of assuming an almost spher- 
ical shape. The intensity of the force of cohesion varies in different 
liquids. 

When a pipe bowl is dipped into soapy water, the cohesion of the 
liquid is shown by the film which remains stretched over the surface of 
the bowl. 

101. Adhesion. — When the force of molecular attrac- 
tion acts on the molecules of different kinds of matter, we 
call the force adhesive attraction to distinguish it from 
cohesive attraction. Thus, the hand, when dipped in 
water, is wet ; here we say the water adheres to the hand, 
because the attraction is exerted between different kinds 
of molecules ; namely, between those of the hand and 
those of the water. Chalk-marks adhere to a blackboard, 
but the molecules of chalk cohere to one another. 

102. Chemical Attraction or Affinity. — Molecular 
attraction is not the same as atomic attraction or chem- 
ical affinity, which holds together atoms and not molecules. 

103. Varieties of Adhesion. — The force of adhesive 
attraction manifests itself in a variety of ways : 

(1.) Between solids. 

(2.) Between liquids. 

(3.) Between solids and liquids. 

(4.) Between solids and gases. 

(5.) Between liquids and gases. 

104. Adhesion between Solids. — The resistance to 
motion, produced by friction, is caused not only by the 
irregularities of the surfaces, but also by the molecular 
attraction which such surfaces exert on one another. 

Cements afford examples of adhesion between different 
kinds of solids. Thus, mortar adheres to stones or bricks 
and so binds them together. Glue adheres to the pieces 
of wood or cloth between which it is placed. Paste or 
gum causes paper to adhere to walls. Dried paint ad- 
heres to wood-work, and ink-marks to paper. 



70 NATURAL PHILOSOPHY. 

105. Adhesion between Liquids is seen in the mix- 
ing of different liquids; in the solution of one liquid by 
another; and in the diffusion of liquids. 

1. Mixture. — Oil and water will not mix, because there 
is not sufficient adhesion between their molecules. The 
same is true of mercury and water. Milk and water, how- 
ever, mix readily, because the molecules of the one adhere 
to those of the other ; and the same is true of many other 
liquids. 

2. Solution. — The solution of one liquid by another may 
also be regarded as a species of adhesion. Thus, castor- 
oil is dissolved by alcohol. Many cases of solution, how- 
ever, are caused by the influence of a partial chemical 
attraction. Thus, pure concentrated alcohol and water 
combine chemically, but a weak solution of alcohol mixes 
with water in any proportion. 

3. Diffusion. — If a vessel filled with liquid be carefully 
lowered below the surface of some lighter liquid with 
which it is capable of mixing, though no agitation has 
occurred, yet after a time, the two liquids will be found to 
have thoroughly mingled, as much of the heavier liquid 
being now found in the upper portions of the vessel as in 
the lower. Phenomena of this kind are known under the 
general name of diffusion. 

106. Adhesion between Solids and Liquids. — 

1. Wetting. — When plunged into water, the hand be- 
comes wet, because the water adheres to it ; but if plunged 
into mercury the hand is not wet, because there is but 
little adhesion between it and the mercury. Water-proof 
fabrics contain substances that are not readily wet by 
water. When rain falls on such fabrics, it either falls off, 
or can be easily shaken off. 

2. Solution. — When a lump of sugar is thrown into a 
glass of water, the sugar gradually disappears and be- 
comes mixed throughout the liquid, which acquires a 
sweetish taste. The adhesion of the water and the sugar 



COHESION AND ADHESION. 



71 



results in the breaking of the mass of sugar into its con- 
stituent molecules, which are then distributed throughout 
the liquid. We call this change solution. By solution a 
solid becomes changed into a liquid. 

The solvent power of water is much greater than that of nearly any 
other common liquid. As a rule, the solvent power of any substance 
increases with the temperature ; thus, hot water will dissolve more sugar 
than cold water. This, however, is not always the case ; cold water will 
dissolve more lime than hot water. 



107. Capillarity.— If a tube A, Fig. 26, of large diam- 
eter, be dipped into a liquid which wets it, the liquid will 

stand as high outside of the tube 

as inside; but if the tube be of 

smaller diameter, as at J5, and 

the liquid wets the tube, it will 

rise higher inside the tube than 

outside of it. If the tube be still 

smaller, as at (7, the liquid* will rise 

higher than at B. The surface of 

the liquid in all the tubes will be 

concave as shown in the figure. 

When the liquid does not wet the walls of the tube, if 

the tube be of large diameter, as shown at 2?, Fig. 27, the 

level inside is the same as 
that outside ; but if the dia- 
meter be small, as at F, the 
liquid will be depressed with- 
in the tube, so that the level 
on the inside of the tube will 
be lower than that on the 
outside, and the free surface 
of the liquid will be convex. 
In a tube of still smaller 

diameter, as at 6r, the depression will be greater than 

at F. These phenomena are called capillary phenomena. 




Fig. 26.— The Liquid Wets 
the Tube. 



E 



G 




Fig. 27.- 



-The Liquid does not Wet 
the Tube. 



72 NATURAL PHILOSOPHY. 

A capillary tube is one whose diameter is small or 
hair-like. 

Capillarity deals with the elevation or depression of liquids 
in tubes of small diameter. 

The principal phenomena of capillarity are, 

(1.) A liquid rises in a capillary tube when it wets 
the tube, but is depressed when it does not wet the 
tube. 

(2.) The amount of the elevation or depression is greater 
as the diameter of the tube decreases. 

(3.) The amount of elevation or depression varies with 
the kind of liquid. 

108. Surface Tension. — Below the surface of a liquid 
mass, the molecules being attracted in all directions by 
the surrounding molecules, possess great freedom of mo- 
tion. At the surface of a liquid, however, the molecules 
being attracted only by the molecules below them, have 
comparatively little freedom of motion, the liquid acting 
as though a thin skin or film was stretched over its sur- 
face. The tension so produced at the surface of a liquid 
is called surface tension. 

The surface tension on the liquid contained within the film, tends to 
reduce the contained liquid to the shape in which its free surface shall 
have the least area ; i. e. the spherical shape. This is the reason a soap- 
bubble assumes a spherical form ; or the drop of melted lead, allowed to 
fall from a shot tower, assumes the spherical form of shot. 

Experiment 28. — Blow a soap-bubble by means of a pipe in the 
usual manner. Observe, that though the bubble may not be truly spher- 
ical while being blown, yet as soon as the blowing ceases, its surface ten- 
sion causes it to assume a spherical shape. 

109. The Cause of Capillary Phenomena. — Capillary 
phenomena result from the difference between the cohesion 
of the liquid molecules for one another, and their adhesion 
to the walls of the capillary tube. 



COHESION AND ADHESION. 73 

Capillary phenomena may be regarded as due to surface tension, modi- 
fied by the adhesion of the liquid to the walls of the tube ; since, how- 
ever, surface tension is the result of cohesion, the phenomena of 
capillarity result from the cohesion of the molecules of a liquid to 
one another, and their adhesion to the walls of the capillary tube. 

A liquid rises in a capillary tube which it wets, because 
the adhesion between the liquid and the walls of the tube 
draws the liquid towards the walls of the tube. A liquid 
is depressed in a capillary tube which it does not wet, be- 
cause the cohesion of the liquid draws it away from the 
walls of the tube. If the liquid wets the tube, the adhe- 
sion between it and the tube, or the force which draws 
the liquid towards the walls, is greater than the force of 
cohesion, which tends to keep the particles of the liquid 
together. If the liquid does not wet the tube, the force 
of cohesion is greater than that of adhesion. 

110. Familiar Examples of Capillarity. — The phe- 
nomena of capillarity occur in loose, porous substances, 
whenever the spaces, or sensible pores, between the par- 
ticles are of capillary dimensions. Thus oil rises in the 
wick of a lamp, through the capillarity of the spaces be- 
tween the strands. A lump of sugar, placed with only 
its lower end in milk or water, is soon wet throughout ; 
here the elevation of the liquid is due to capillarity. A 
towel, hung so that only its lower end dips in water, is 
soon wet for a considerable distance above the level of the 
water, from the same cause. 

111. Osmose is the unequal mixing of two different 
liquids through the pores of a membranous substance 
which separates them. 

Two liquids, capable of mixing with each other, placed 
in compartments of the same vessel, separated only by a 
thin wall of bladder, or other suitable membrane, through 
the pores of which the liquids can pass slowly, will not 
remain separate, but will mix with each other. This mix- 



74 



NATURAL PHILOSOPHY. 



ing, however, is different from that produced by mere dif- 
fusion. If, for example, sugar and water be placed in one 
compartment, and pure water in the other, it will be found 
that more of the pure water will pass into the compart- 
ment containing the sugar and water, than will the sugar 
and water into the other compartment. After standing 
for several hours, therefore, the level of the liquid will 
be higher in the compartment containing the sugar and 
water. 

Experiment 29.— Fill a bladder B, with a saturated solution of 
sugar and water, colored with indigo or aniline. Tie the bladder to 
the lower end of a glass tube T, and support 
bladder and tube in a vessel C, filled with 
pure water, in the manner shown in Fig. 28, 
so that the level of the colored water in the 
tube T, is the same as that of the water in C. 
Observe, that at the end of several hours, 
the colored liquid mounts in the tube, and 
that the water in C, becomes colored. A 
flow both from and into the bladder has taken 
place through the pores of the bladder. The 
flow of the water into the sugar solution, 
however, has been greater than the flow of 
the sugar solution into the water, as shown 
by the higher level in the tube. This dif- 
ference of flow will continue for several days. 
The flow towards the higher level is some- 
times called the endosmotic flow; that to- 
exosmotic flow. There are, therefore, two 




Fig, 28.— Endosmometer, 



wards the lower level the 

varieties of osmose ; viz., endosmose and exosmose. 

112. Dialysis. — Substances differ in their power of pass- 
ing through a membranous wall. Crystallizable substances, 
or crystalloids, such as sugar and common salt, as a rule, 
pass freely through such a wall; while uncrystallizable 
substances, or colloids, such as gums, glues, or jellies, do 
not pass at all. 

Graham, a distinguished chemist, based on this fact a process, called 
dialysis, for the separation of crystalloids from colloids. A mixture of 
the colloids and crystalloids to be separated was placed in the dialyser, 
consisting of a vessel, the bottom of which is formed of a sheet of arti- 



COHESION AND ADHESION 75 

ficial parchment paper floated in a vessel of pure water. In a few days 
the crystalloid substances had passed through the dialyser into the water, 
while the colloids had remained in the dialyser. Arsenious acid, a crys- 
talline substance, may be separated in this way from substances contain- 
ing it. 

113. Adhesion between Solids and Gases. — Adhe- 
sion between solids and gases is seen in the absorption of 
gases by solids. Charcoal has a wonderful power of ab- 
sorbing various gases and condensing them within its 
pores. Freshly burned charcoal can absorb nearly a hun- 
dred times its own bulk of some gases. When thrown on 
decaying animal or vegetable substances, it removes most 
of their bad odors by absorbing the malodorous gases as 
fast as they are given off. The smell of tobacco clings for 
some time to the clothes of one who has been smoking. 
This is due to the adhesion between the smoke and the 
clothes. 

114. Adhesion between Liquids and Gases. — 

Experiment 30. Place a few drops of aqua-ammonia in a test- 
tube and apply heat until it begins to boil. Quickly invert the tube in a 
tumbler of water. Observe that the water rises in the test-tube as the 
ammonia vapor is absorbed by the water. 

Most liquids have the power of absorbing various gases. 
Water possesses this property in a remarkable degree. All 
water, which has been exposed for some time to the air, 
will be found to contain a considerable amount of air in 
solution. If a tumbler of clear water be allowed to stand 
for some time, minute bubbles of gas will collect on the 
inside of the glass. These bubbles come from the air 
which was dissolved in the water. 

If a tumbler of water be placed under the receiver of an 
air pump and a vacuum be made in the receiver, the air 
in the water will escape in a stream of bubbles. 

115. Properties Peculiar to Solids. — The solid con- 
dition of matter is characterized by certain properties 



76 NATURAL PHILOSOPHY. 

peculiar to it. The most important properties peculiar to 
solids, are malleability, ductility, hardness, brittleness, 
tenacity, elasticity of ftexure or torsion, and crystalline 
form. 

116. Malleability is the property certain solids possess 
of being wrought into different shapes under the hammer 
or roller. The molecules of malleable bodies possess the 
power of flowing or moving over one another under the 
hammer or roller. Most of the metals are malleable to a 
certain extent, and on this property much of their value 
depends. Gold is the most malleable metal known. It 
can be beaten into leaves so thin, that it takes 300,000 
such leaves to make a pile one inch in thickness. The 
malleability of metals under the hammer is somewhat 
different than under the roller. Gold, lead, silver, tin, and 
copper are very malleable. 

117. Ductility is the property certain solids possess of 
being drawn out into wire. This property is possessed 
generally by the metals, and is nearly the same as mal- 
leability, since in both, the molecules of the body, when 
subjected to pressure or strain, are caused to flow or 
move over one another without fracture occurring in the 
metal. The different metals, however, are not malleable 
and ductile to the same extent. 

Platinum, silver, iron, and copper are very ductile. 

118. Hardness is that property by which certain sub- 
stances resist being scratched or worn by others. We can 
tell which of two substances is the harder, by rubbing 
them together ; that which is the harder will scratch the 
other. The terms hard and soft are relative, since a body 
which is hard, when compared with one substance, may 
be soft when compared with another ; thus, glass will 
scratch marble ; therefore, glass is hard when compared 
with marble, but the diamond will scratch glass, so that 
glass is soft when compared with the diamond, 



COHESION AND ADHESION. 77 

A scale of hardness is made by arranging a number of mineral sub- 
stances in such an order that each is readily scratched by any mineral 
following it, but itself scratches any which precedes it. Such a table 
is as follows : 

1. Green laminated talc. 6. Cleavable feldspar. 

2. Crystallized gypsum. 7. Transparent quartz. 

3. Transparent calc spar. 8. Transparent topaz. 

4. Crystalline fluorspar. 9. Cleavable sapphire. 

5. Transparent apatite. 10. Diamond. 

This table is used as follows ; flint scratches quartz with difficulty, 
but is readily scratched by topaz. Its hardness is, therefore, taken arbi- 
trarily as say, 7.5, or of intermediate hardness between topaz and quartz. 

In the sand-blast process, a stream of fine sand, driven by 
a jet of air or steam, is used to cut designs on glass, or to 
cut through hard metals. 

119. Hardening, Annealing, Tempering. — Certain 
metals possess the remarkable property of having their 
hardness changed by heat. If they are heated about to 
redness, and then suddenly cooled by being plunged into 
cold water, they become hard and brittle. Steel possesses 
this property in a remarkable degree. The process is 
called hardening. 

When steel is highly heated and allowed to cool slowly, 
it becomes soft, ductile, and malleable. This process is 
sometimes called softening or annealing. 

If a bar of hardened steel is struck a sharp blow with a hammer, it 
is apt to be fractured; but if softened, it may be wrought into any 
desired form, such as a knife-blade, an axe, or a hatchet, and these 
articles may afterward be hardened by high heating and subsequent 
rapid cooling. As a rule, the hardness so obtained is so great that the 
articles would be too brittle for use ; in this case a portion of the hard- 
ness may be removed by heating to a lower temperature, and then 
allowing them to cool. This process is called drawing the temper. 

The causes of these curious properties are not known except that they 
are connected with a re-arrangement of the molecules. 



78 NATURAL PHILOSOPHY. 

120. Brittleness. — A substance is brittle when it is 
readily broken into pieces. This property is almost the 
opposite to that of malleability. Brittle substances are 
generally hard. 

121. Tenacity. — By the tenacity of a substance is meant 
its power to resist being pulled apart. The tenacity of a 
body is due to the cohesion of its molecules, and, as cohe- 
sive attraction varies greatly in different substances, the 
tenacity must always vary. 

If the force tending to pull the molecules apart is applied in the direc- 
tion of the length of the body, the tenacity must increase with the area 
of transverse section, that is, a section made at right angles to the length ; 
for, if of the two bars, A and J5, 

Fig. 29, of the same material, -*> / 

A, has a smaller area of trans- 





Fig. 29.— Influence of Sectional Area on Tenacity. 

verse section, abed, than efg h, of B, then the total tenacity of A, must 
be less than that of B, since there are fewer molecules in any cross sec- 
tion of A, tending to hold the bar together than there are in any cross 
section of the larger bar B. If, then, the area efgh, be four times as 
great as a b c d, the bar B, would require four times as great a force to 
pull it apart as the bar A y and so also with any other proportion of 
areas. 



The tenacity of a bar or beam is independent of its 
length. The increase in the length does not affect the 
number of molecules in any area of cross section. But 
the greater the length of the beam the greater the proba- 
bility of a flaw or a weak spot, so that a long beam is likely 
to have less tenacity than a short beam, and would, of 
course, break at its weakest part. Since, however, the 



COHESION AND ADHESION. 79 

weight of the beam tends to break it, we can see that the 
breaking weight is less as its length increases. 1 

122. Elasticity is that property of a body by which it 
resists change of shape, and returns to its original shape 
when the distorting force is withdrawn. 

Elasticity in any body necessities its possession of two 
properties ; viz., resistance, by virtue of which a force is re- 
quired to change its bulk or shape; and restitution, by 
virtue of which the continued application of the distort- 
ing force is required to maintain a change of shape, the 
body tending to resume its former bulk and shape as soon 
as such force is withdrawn. 

All kinds of matter, whether solid, liquid, or gaseous, 
when compressed, will tend, to some extent, to regain their 
original bulk, or, in other words, possess elasticity. 

Elasticity developed in a body by compression is, there- 
fore, a general property of matter. 

There are two general varieties of elasticity ; viz., elas- 
ticity of form or shape, and elasticity of volume or bulk. The 

1 Table of Tenacity (per Unit of Cross-section). 

Kilogrammes 

Lbs \P er persq. 

sq. m. millimetre. 

Wrought Iron 56,900 40 

Cast Iron 17,780 12.5 

Tempered Steel 106,700 75 

Copper Wire 29,870 21 

Brass 17,640 12.4 

Bronze 36,420 25.6 

Zinc 7,480 5.26 

Lead 1,850 1.3 

Tin 4,980 3.5 

Aluminum 28,880 20.3 

Glass 9,220 6.48 

Brick and Cement 285 0.2 

A s h 16,670 11.72 

s P r uce 12,160 8.55 

Oak 14 ? G00 10.26 



80 NATURAL PHILOSOPHY. 

former is possessed by solids only ; the latter is possessed 
both by solids and fluids. 

Solids are the only form of matter which can be stretched, 
bent, or twisted. Elasticity is developed by any of these 
changes. 

Elasticity developed in a body by stretching, bending, 
or twisting, is, therefore, a property peculiar to the solid 
condition of matter. 

Elasticity of form, developed by stretching or tension, is seen in the 
return to its former length of a piece of caoutchouc, or India-rubber, 
or, in a lesser degree, in a wire after it has been stretched by a weight. 
Elasticity developed by bending or flexure, is seen in the recoil of a bow 
which has been bent and then released. Elasticity developed by twist- 
ing or torsion, is seen in the untwisting of a string or wire which has 
been twisted. 

123. The Measure of Elasticity. — The degree of elas- 
ticity of a body is measured by the force with which it 
tends to regain its original shape or bulk when that shape 
or bulk has been changed by compression, stretching, bend- 
ing, or twisting. Liquids and gases, as a rule, when com- 
pressed, resume their original volume on the removal of 
the pressure, and, therefore, possess perfect elasticity of 
volume. Within certain limits of compression, nearly 
every solid body will resume its original shape when re- 
lieved from compression, bending, stretching, or twisting, 
and is therefore elastic ; but with many solids the limits of 
elasticity, or the limit beyond which any further compres- 
sion, bending, stretching, or twisting would produce a per- 
manent change of form, are so small, that they may be 
considered as inelastic. 

124. Crystalline Form. — We recognize an animal or 
plant by a certain form peculiar to it. In the same way 
many lifeless substances occur in forms, called crystals, 
peculiar to them. Although in most solids these crystals 
are too small to be seen, yet they nearly always exist. 
For example, snow is composed of crystals of beautiful 
shapes. 



PROBLEMS. 81 

Crystals are more or less regular in shape, and although 
of many different forms, are all modifications of a few 
simple forms. 

Experiment 31.— Place a quarter of a pound of common alum in as 
much hot water as will completely dissolve it. Strain the solution through 
a piece of muslin, and pour the clear liquid into a cup or bowl, in which 
has been placed a piece of rough stone wrapped with colored yam. Set 
the liquid aside in a quiet place over night, and in the morning, shining 
crystals will be found covering the stone. By slipping a thin knife under 
the stone, it may be readily separated from the bottom of the cup or bowl. 

PROBLEMS. 

1. Assuming that the breaking stress of iron is 56,900 lbs. per 
square inch of cross section, what stress, in lbs. weight, will just 
break an iron wire one-tenth of an inch in diameter ? 

Ans. 446.9 lbs. weight. 

2. A filament of spun glass has a diameter of 0.01 millimetre. 
What would be the tenacity of such a filament, taking 6.48 kilos, 
per square millimetre as the tenacity of glass ? 

Ans. 0.5089 gramme weight. 

3. What cross section of oaken beam having a breaking stress 
of 14,600 lbs. per sq. inch, will give the same tenacity as a circular 
rod of wrought iron one inch in diameter, with a breaking stress 
of 56,900 lbs. per sq. inch. Ans. 3.061 sq. inches. 

4. Which possesses the greater breaking stress, an oaken beam 
ten square inches in area of cross-section, having a tenacity per 
square inch of 14,600 lbs., or an ash beam nine square inches in 
area of cross-section, having a tenacity per square inch of 16,670 
lbs. ? How much greater ? Ans. The ash beam, by 4030 lbs. 

5. How many times greater tenacity has a rod of tempered steel, 
whose area of cross-section is one square inch, than a rod of copper 
of equal cross-section. Ans. 3.57 times. 

6 







CHAPTER VII. 

WORK, ENERGY AND POWER. 

125. Work. — When force is exerted through a distance, 
work is said to be done. 

A car will not move of itself over a level road, but re- 
quires either to be drawn by a horse, steam engine or 
electric motor, or to be pushed by a man. In other words, 
it requires force to act on it through a distance. When it 
is drawn or pushed over a track by any force, the amount 
of work done is measured by the strength of the force 
acting, multiplied by the distance through which it acts. 

Work is never done by a force unless the force produces 
a motion of the body on which it is acting. A weight 
resting on a table produces a pressure on the table, but 
does no work until the force of gravity, which causes the 
pressure of the weight, is permitted to produce a motion 
of the weight ; i. e., to cause it to move or to fall. 

A coiled spring, as in the works of a watch or clock, 
produces a pressure in attempting to uncoil itself, but it 
does no work until the force of elasticity, which causes 
the pressure, is permitted to produce a motion. 

When a body is moved by any force, it is said to have 
work done on it. The moving body causing the motion is 
said to do work on the body it moves. Thus, when a man 

82 



WORK, ENERGY AND POWER. 83 

moves a weight he is said to do work on the weight; 
when a falling weight moves the body which it strikes, 
the weight is said to do work on that body. 

126. Elements of Work. — The elements of work, are, 

1. Force. 

2. Distance. 

Work is measured by the force which is acting, multi- 
plied by the distance through which it acts. If a certain 
effort is required to lift a weight through a distance of 
one foot, it will require twice the amount of work to be 
done to lift this weight through two feet, or through 
twice the distance. 

127. Energy. — The capability of doing work is called 
energy. Whenever any work is done, energy is expended. 
As soon as a body expends its store or amount of energy 
its ability to do work ceases. 

All natural phenomena are caused by energy acting on 
matter. Natural philosophy is, therefore, sometimes de- 
fined, as that branch of natural science which treats of 
matter and energy. 

128. Transfer and Transformation of Energy.— 

Whenever energy is expended to produce a phenomenon, 
such energy must be drawn or transferred from some stock 
or store of existing energy. For example, when the spring 
of a clock is run down, and has thus expended the energy 
it possessed, it requires a new store or stock of energy to 
be again imparted to it ; as by the muscular force of the 
hand that winds it up. When the raised weight has ex- 
pended its energy by falling from the lable to the ground, 
* it requires that energy be again imparted to it, in order to 
raise it from the ground to the table. 

Doing work or expending energy may also consist in a 
transformation of energy from one form to another ; thus 
the man who wound the clock drew his store of energy 
from his food, which, after its assimilation by his body 



84 NATURAL PHILOSOPHY. 

had its chemical energy changed or transformed into mus- 
cular energy. The food, in its turn, received its energy 
by various transformations from the sun. The light emit- 
ted by an electric lamp is obtained by means of a trans- 
formation or change from the energy of the electric cur- 
rent that passes through it. 

The energy required to drive a steam engine is derived 
from the steam. The steam drew this store of energy 
from the coal burned under the boilers. The coal re- 
ceived its energy from the sun during the growth of 
the vegetable matter from which the coal was formed. 
To produce any natural phenomenon an expenditure of 
energy is required. During this expenditure, certain trans- 
formations of energy are produced, energy disappearing in 
one form and reappearing in another form, but in no case 
is any energy lost or annihilated, there being the same 
total amount of energy in the universe after the phenome- 
non has occurred as before. 

129. The Unit of Work generally adopted for com- 
mercial purposes in Great Britain and America is the 
foot-pound , or the amount of work done when a weight of 
one pound is raised vertically through a distance of one 
foot. 

When a weight of one pound is raised vertically through 
the distance of one foot, an amount of work is done equal 
to one unit, or to one foot-pound, because a force equal to 
one pound overcomes a resistance, or raises a weight of 
one pound through the distance of one foot against the 
earth's gravitational pull. 

The unit of distance is taken as equal to one foot. Unit 
work, the foot-pound, is done when unit force acts through 
unit distance. 1 

1 When the French weights and measures are employed, the unit of 
work is the kilogramme-metre, or the amount of work done when one 
kilogramme is raised vertically through a distance of one metre. 
1 kilogramme-metre = 7.233 foot-pounds. 



WORK, ENERGY AND POWER. 85 

The same amount of work is done when ten pounds are 
raised vertically through one foot, as when one pound is 
raised vertically through ten feet, or five pounds through 
two feet, or two pounds through five feet ; viz., ten foot- 
pounds. 

When the work done is different from the raising of a 
weight, such as sawing a log of wood, or crushing a lot 
of ore, it is convenient to express the amount of work 
done in foot-pounds, as in raising a weight. This may 
always be done, since all work requires force to act 
through distance. 

130. Power, Activity, or Rate-of-doing-Work. — 

By power or activity is meant the rate-o$-doing-work. 

A careful distinction must be drawn between the total 
expenditure of energy or the work done, and the rate at 
which this energy is expended, or the power. 

Apart from the resistance of the air, the same amount 
of work is done in raising 100 pounds through one foot ; 
viz., 100 foot-pounds, whether it be done in one second, in 
one minute, or in one hour. The rate at which the work 
is done, or the rate at which energy is expended in doing 
the work is, however, quite different, being sixty times 
greater if done in one second, than if done in one minute. 

The unit of power is the foot-pound-per-second, or an ex- 
penditure of energy at the rate of one foot-pound per 
second. 

131. Horse Power. — Another practical unit or rate of 
doing work, employed in America and England, is the 
horse-power, a rate of doing work equal to 550 foot-pounds- 
per-second, or 33,000 foot-pounds-per-minute. 

132. The Centimetre-Gramme-Second, or the C. 
G. S. System of Units. — Besides the preceding units 
of force, work and power, scientific men generally adopt 
a system based on the centimetre as the unit of length, 
the gramme as the unit of mass, and the second as the 



86 NATURAL PHILOSOPHY. 

unit of time. For this reason these units are called the 
Centimetre- Gramme-Second Units, or briefly the 0. G. S. 
units. 1 

133. Potential and Kinetic Energy. — A pound weight 
attached to a cord passing over a pulley, requires ten foot- 
pounds of work to be done on it to raise it through a ver- 
tical distance of ten feet. If the raised weight be secured 
in position by fastening the end of the cord, the ten foot- 
pounds of energy are stored in the weight, and the energy 
so stored is called potential energy. 

When the cord is cut, the weight falls and when it 
reaches the ground it has acquired a velocity such as will 

1 The C. G. S. unit of force is called the dyne. It is a force of such 
an intensity, that acting for one second on a mass of one gramme, will 
impart to it a velocity of one centimetre per second. 

At the latitude of Washington, D. C, the force of gravity on one 
gramme is equal to about 980 dynes. 

The 0. G. S. unit of work is called the erg, and is equal to a dyne cen- 
timetre, or the amount of work done when one dyne acts through the 
distance of one centimetre. 

Since gravity acts on one gramme with a force of 980 dynes, when 
one gramme is raised vertically one centimetre, the amount of work 
done is, approximately, equal to 980 dynes, multiplied by one centi- 
metre = 980 dyne-centimetres, or 980 ergs. 

One foot-pound equals 13,560,000 ergs, approximately. As the erg 
is so inconveniently large a number, ten million ergs are taken as the 
practical unit of work in the C. G. S. system. This unit is called the 
joule. 

1 foot-pound = 1.356 joules. 

1 joule = 0.7373 foot-pounds. 

The C. G. S. unit of activity is the erg-per-second. The practical unit 
of activity is the watt, or the joule-per-second, or a rate of expending 
energy equal to one joule-per-second. The watt is equal to 0.7373 foot- 
pounds-per-second. 

1 Horse Power (British) = 550 foot-pounds-per-second. 

1 " " " = 33,000 foot-pounds-per-minute. 

1 " " (French) = 75 kilogramme-metres-per-second. 

1 " " " = 4500kilogramme-metres-per-minute. 



WORK, ENERGY AND POWER. 87 

enable it to do an amount of work exactly equal to that 
expended on it in raising the weight to that distance of 
ten feet. This energy of motion is called kinetic energy. 

134. Convertibility of Energy. — When a ball is 
thrown vertically upward, all the energy it possesses at 
the moment it leaves the hand is kinetic; as the ball 
rises its energy gradually becomes potential, and, when it 
reaches the highest point of its ascent, all its energy is 
potential. As it falls, its potential energy gradually be- 
comes kinetic. At any point, either of its ascent or 
descent, the sum of its kinetic and potential energies is 
a constant quantity. 

This alternate change of energy from kinetic to poten- 
tial, or from potential to kinetic, naturally follows from 
the indestructibility of energy. 

135. Relation of Energy to Velocity. — The energy 
possessed by a body moving with a certain velocity may 
be estimated by determining the vertical height to which 
such velocity would raise it against the force of gravity. * 
We can thus express the energy the body possesses in 
any of the units of work. 

The power of a moving body to do work is increased by an increase 
of its velocity. 

The amount of kinetic energy possessed by a moving body may always 
be determined by multiplying half its mass by the square of its velocity. 

136. Machines. — A machine is any arrangement of 
parts, by means of which, force is so transmitted from one 
point to another that either its intensity, or its direction, 
or both, are modified. The work done by the force which 
moves or drives a machine, is called the moving or driving 
force. The work to be done, is called the work, weight, load, 
or resistance. 

Disregarding friction, in all machines the work done by 
the driving force is always equal to the work done on the 
resistance or resistances. 



88 



NATURAL PHILOSOPHY. 




Fig. 30— A Simple Machine. 



A pair of scissors, Fig. 30, affords a good example of a 
simple machine. Here the driving force, which is the 

muscular force of the fingers, 
is applied at the handles, in 
a direction which causes the 
handles to come together. 
The work done by the scis- 
sors is the cutting of some material placed between the 
two blades. 

The lever, or inflexible rod A B, shown in Fig. 31, is 
another example of a simple machine. If the lever sup- 
ported on the point 
F, nearer A than B, 
be moved until it as- 
sumes the position, 
A f B' then the dis- 




Fig. 31,— A Simple Machine. 



tance B B', through 

which the end B, 

moves, will be greater than the distance A A', through 

which the end A moves, in proportion as the distance 

FB, is greater than the distance FA. 

If the distance FB, is 2i times as great as FA, then a 
force of one pound weight applied at B, will raise 2i 
pounds at A, or conversely, a force of 2J pounds at A, will 
raise one pound at B. 

These two forces balance each other because the work 
done at one end of the lever equals the work done on the 
other end. When, for example, a force at B, balances a 
force at A, the work done by B, exactly equals that done 
by A. Suppose, for example, the lever be used to raise a 
stone through the distance A A\ equal to one vertical 
foot. Then a force of 100 pounds applied at 2?, will raise 
a weight of 250 pounds at A. To do this, the end jB, moves 
through the distance B B\ of 2J feet. But a weight of 
100 pounds raised through a space of 2} feet equals 250 
foot-pounds of work, and this is exactly equal to the work 



WORK, ENERGY AND POWER. 89 

done on A ; viz., 250 lbs. raised through the space of one 
foot, or 250 foot-pounds. 

In general, equilibrium will result in any machine when 
the power multiplied by the space through which it moves, 
is equal to the resistance multiplied by the space through 
which it is moved. 

This principle will enable us to determine the relation existing be- 
tween the work expended in driving any machine, and the work done 
by the machine ; for, disregarding friction and fluid resistances, we have 
only to notice that the work done by the driving force must equal the 
work done against the load. Suppose, for example, in any machine, 
that work is being done on it at the rate of 10 foot-pounds per second, 
and that [the load is one pound weight, then if no work is expended 
within the machine, the output must be 10 foot-pounds per second, and 
the weight, if lifted vertically, will be raised 10 feet per second. 

137. No Machine Creates Energy. — Since in every 
machine the work done by the driving force is always equal 
to the work done on the resistance, it is clear that no machine 
creates energy. A machine may increase the intensity of the 
working force, but can never increase the amount of energy. 

In the preceding example, Fig. 31, a force of 100 pounds 
weight applied at B, overcame a resistance of 250 pounds 
weight at A. This gain, however, was at the expense of 
the distance through which it moved ; for the weight at 
A, moved 2J times more slowly than the power at B. 
Therefore, what a force gains in intensity, it loses in the distance 
through which it moves. 

If a weight of 250 pounds be applied at the end A, it 
will raise a weight of 100 pounds at B, but it will raise it 
2J times more rapidly. Therefore, what a force loses in in- 
tensity, it gains in the distance through which it moves. 

Although a machine gains nothing in energy, it may gain consider- 
ably in convenience. To make this clear, suppose that, by exerting his 
entire strength, a man could lift just 300 pounds. Then, by the use of 
a machine, such as a lever, he could raise say 300 x 10 = 3000 lbs. ; but 
to raise these three thousand pounds through one foot, he would be re- 
quired to exert a force of three hundred pounds weight through ten 



90 NATURAL PHILOSOPHY. 

feet ; and this would clearly be the same as if he divided the three 
thousand pounds into ten separate parcels of three hundred pounds each, 
and, for ten successive times, exerted his strength of three hundred pounds 
through a single foot. 

In general, whatever be the nature of the work for which the machine 
is designed, its perfection depends on the convenience it secures in the 
performance of that work. 

138. Advantages Gained by Machines. 

1. Machines may enable us to increase the effective in- 
tensity of a force by causing it to move with a smaller 
velocity ; or, they may enable us to obtain an increased 
velocity at a corresponding expense of intensity. 

2. Machines may enable us to change the direction in 
which the power is applied, thus affording a great con- 
venience. For example, a cord passed over a^pulley may 
be applied more advantageously for the raising of a weight 
than by raising the weight directly. 

3. Machines may enable us to apply other forces than 
our muscular force, such as the force of the wind, of 
running water, or of steam power. 

139. Laws of Machines. — The work done by any 
machine consists of two distinct parts : 

1. The useful work or the output; i. e., that done by the 
machine in performing the work for which it was de- 
signed. 

2. The useless or wasted work, or that done by the ma- 
chine against the friction of the moving parts or the re- 
sistance of the air. 

The sum of the useful and wasted work must be equal 
to the work expended in driving the machine, or the intake. 

The efficiency of a machine is the quotient obtained by 
dividing the output by the intake. An efficiency of 0.95 
or 95 per cent, indicates that 5 per cent, of the power is 
wasted in internal work. Therefore, the smaller the waste, 
the greater the efficiency of the machine. The efficiency 
can, of course, never exceed 100 per cent. 

140. The Mechanical Powers are the lever, the wheels 



WORK, ENERGY AND POWER. 91 

and axle, the pulley, the inclined plane, the wedge, and the 
screw. 

These six mechanical powers are, in reality, modifica- 
tions of the lever and the inclined plane. 

In the following statements relative to simple machines, it is, for con- 
venience, assumed that no energy is wasted during its transmission from 
one part of the machine to another. 

141. The Lever. — A lever consists of an inflexible 
rod or bar moving about a fixed point, called the fulcrum. 

A force applied at one end of 

the lever overcomes a resistance, ^™^^ 

or lifts a weight, at another part. P i 

The different forms of levers w 

i j • j. i i Tig, 32.— Lever of the 1st Class. 

may be arranged in three classes, 

according to the relative positions p 

of the fulcrum, and the points 

■I'niM..ir,i. ■ « 



of application of the force and |T 
of the weight. 

In levers of the first class, Fig. r , M ^ „ .. , n 

' & Fig. 33— Lever of the 2d Class. 
32, the fulcrum is between the 

force and the weight ; in levers of the second class, Fig. 33, 

the weight is between the fulcrum and the force ; and in 

levers of the third class, Fig. 34, the force is applied 

between the fulcrum and the weight. 

Examples of levers of the first class are found in a pair 
of scissors ; in a crowbar, when used to raise blocks of 
stone ; in the common balance for weighing, and in a pair 
of pincers. 

Examples of levers of the second class, are found in 
nut-crackers, Fig. 35, where W, p 

the nut to be cracked, is placed a 

between the fulcrum F, and the E 

part P, where the force is ap- ' — " ' ilip ^ 

plied. A door, when opened by W 

the hand applied to the knob, Tig. 34.-Lever of the 3d Class. 

is another example ; the weight of the door is between the 



92 



NATURAL , PHILOSOPHY. 



hinges, which act as the fulcrum, and the knob, the point 

where the power is ap- 
plied. A wheelbarrow is 
another example. 

Examples of levers of 
the third class are found 




Fig. 35.— Levers of the 2d Class. 



in the sugar-tongs, Fig. 36 ; in the fire-tongs ; and in the 
common foot-treadle. 



142. Advantage of a Lever 

the effects produced by 
any lever, we must know : 

1. The points of appli- 
cation of the force and of 
the resistance or weight. 

2. The position of the 
fulcrum; or, in other words, 



-In order to calculate 




Fig. 36.— Sugar-Tongs. 



the relations existing between the arm of the force and the 
arm of the weight. 

The arm of the force is the shortest distance from the ful- 
crum to the direction in which the force acts. The arm of 
the weight is the shortest distance from the fulcrum to the 
direction in which the weight acts. 

When the force acts, as in Fig. 37, in a direction, B P, at right angles 
to the length of the lever, then F B, is the arm of the force ; but, if it 




P' 

Fig. 37— The Arms of a Lever. 

acts in any oblique direction, as BP\ then FB', the shortest distance 



WORK, ENERGY AND POWER. 93 

from the fulcrum to the direction B / P', of the force, is the arm of the 
force. 

143. Compound Levers. — Where it is desired to obtain 
a very great difference between the length of the arm of 
the force and the arm of the weight, in order to avoid in- 
convenience, a number of levers are employed, in w r hich 
the arm of the resistance in the first lever acts directly 
against the arm of the force on the second ; and the arm 
of resistance of the second, against the arm of the force 
of the third, and so on throughout all the levers. Hay 
scales usually employ compound levers. 

144. The Wheel and Axle.— In the wheel and axle, 
force applied at the circumference of a wheel is employed 
to raise a weight attached to a rope wound around the 
axle. Fig. 38, show T s a form of wheel and axle called the 
windlass. The force, ap- ^ 

the axis, the arm of the . 

r . ' ,. , Fig. 38 —The Windlass, 

iorce is the radius of 

the wheel, and the arm of the weight is the radius of the 
axle. 

Since, by one complete turn of the wheel, the weight is 
raised only the length of the rope wound once around the 
axle, a force of a pound weight applied at the wheel, will 
raise a weight of as many more pounds, hung to the axle, 
as the circumference of the wheel is greater than the cir- 
cumference of the axle. 

Thus, if the handle TT, of the windlass shown in Fig. 38, be at a dis- 
tance of two feet from the axis, and if the radius of the barrel, on which 



94 



NATURAL PHILOSOPHY. 



the rope is wound, be three inches, then the leverage of the windlass 
will be - 2 /- or 8 to 1, and the hand must move through eight times 
the distance through which the bucket moves. If the bucket weighs 
100 lbs. and be lifted through a total distance of 100 feet, the work done 
will be 10,000 foot-pounds and the hand will be moved through 800 feet 
with a force of 12.5 lbs. weight, making the work done by the hand, 
disregarding friction, 10,000 foot-pounds. 

Water wheels and steering gear for vessels employ the 
principle of the wheel and axle. 

145. The Pulley consists of a wheel turning on its axis, 
and having an edge over which a flexible band or rope 
passes. Pulleys may be fixed or movable. The fixed pulley 
is shown in Fig. 39. 

The pulley, like the wheel and axle, may be consid- 
ered as a continuous lever, the fulcrum of which is at F. 
The arms of the weight and force 

t Fw and Ff, are equal to each other, 

so that no advantage is gained except 
as to the direction of the motion, since, 
if the rope is pulled down one foot by 
the power, it will raise the weight 
through an equal distance. In prac- 
tice, owing to the existence of friction, 
the force applied by the hand must be 
greater than the force exerted by the 
weight. 

In the movable pulley, Fig. 40, the 
block or frame A, to which the weight is attached, is mov- 
able. If the force P, moves downwards and through two 
feet, the weight W, would be raised through but one foot, 
since the rope is moved from both Oand D. In such a 
pulley, therefore, a force of one pound at P, would raise 
a weight of two pounds at W. The fixed pulley is a con- 
tinuous lever of the first class with equal arms. 

Like the wheel and axle, or the lever, pulleys are sometimes com- 
pounded. In the compound pulley, shown in Fig. 41, which contains 



F 



Fig. 39— Fixed Pulley. 



WORK, ENERGY AND POWER. 



95 



three movable and three fixed pulleys, in order to raise the weight one 
foot the force must move through twice as many feet as there are mov- 





Fig. 40.— A Movable Pulley. Fig. 41.— Compound Pulley. 

able pulleys, or through six feet, and one pound at P, will therefore 
balance (neglecting friction) 6 lbs. at W. 

146. Trains of 'Wheel-work. — Where it is desired 
to obtain a considerable difference between the diameter 
of the wheel and the diameter of the axle, a number of 
smaller wheels and axles are combined into what is called 
a train of wheel-work. 

The power applied to the first wheel transmits its effects 
to its axle, which acts on the second wheel, and the axle 
of the second wheel transmits its effects to the next wheel, 
and so on, throughout the entire train. 

Equilibrium results when the force, multiplied by the 
continued product of the radii of all the wheels, equals 
the weight, multiplied by the continued product of the 
radii of all the axles. 

A train of wheels is shown in Fig. 42. The wheel 
on which the driving force is applied is called the driver. 
The wheel on which the power is received is called the 



96 



NATURAL PHILOSOPHY. 



driven wheel, or the follower. 




Pig, 42,-Train of Wheels. 



If, as in the figure, the radius 
of each wheel is six and its 
axle one, then, disregarding 
friction, one pound at P, will 
balance 216 pounds at W. 

Trains of wheel-work are 
used either where great 
weights are to be lifted by 
a small power, as by cranes, 
or, for the purpose of ob- 
taining differences in the 
velocity, as in clock-work. 



In machine shops, the power 
which drives the lathes, planers, 
drills or other tools is transmitted 
from a line of shafting, by means 
of a belt passing rigidly over from a wheel or pulley on the line shaft 
to a pulley on the driving shaft of the machine to be driven. 

147. The Inclined Plane. — Instead of raising a weight 
directly through a given height, it may be raised gradu- 
ally through the same height, by moving it up an inclined 
plane. In this way heavy casks or barrels are moved out 
of deep cellars. 

An example of the inclined plane is seen in Fig. 43, 
where, to raise the barrel through a height equal to the 

height of the plane, we must 
roll the barrel over the whole 
length of the plane. Or, the 
force to be applied to raise 
the barrel must be equal to 
the weight multiplied by 
the height of the plane, di- 

Fig. 43.-An Inclined Plane, vided by ^ length> 

If the length of an inclined plane be four times as great 
as its height, a force of one pound weight will be able to 
move a weight of four pounds up the plane. 




WORK, ENERGY AND POWER. 



97 




1+8. The Wedge. — The wedge is a modified form of 
inclined plane, in which, instead of moving the weight up 
the plane, the plane is moved under the weight. The 
wedge is used when great force is to be exerted in a small 
space, as in splitting wood or stone, Fig. 44, or in press- 
ing oils or juices from seeds. The edge 
of such cutting tools as scissors, knives, 
chisels, hatchets, and razors are forms of 
wedges. 

149. The Screw is another modifica- 
tion of the inclined plane, and bears the 
same relation to a simple plane that a 
spiral staircase does to a straight staircase. Flg ' 44, The Wed s e - 
If a piece of paper be cut in the form of a right-angled tri- 
angle and wrapped around a pencil, as shown in Fig. 45, 
the edge of the paper, which corresponds 
to the length of the plane, will form a 
spiral line around the pencil, in a direc- 
tion w T hich will be the same as that of the 
thread of a screw. As the force which 
turns the screw moves it through one com- 
plete turn, the screw, and anything against 
which it is pushing, as, for example, the 
movable plate of a copying press, Fig. 46, 
advances through the distance between two consecutive 
threads. If the power acting on a screw moves through 
a circumference of 24 inches, 
and the distance between any 
two consecutive threads be y 1 -^ of 
an inch, a force of one pound 
applied at the head of the 
screw would move a weight of 
240 pounds at the other end, 
since the power would move 
through a distance 240 times 
as great as that through which 
7 




Fig, 45. The Prin- 
ciple of the Screw. 




Fig. 46. A Copying-Press. 

the weight moves. 



98 NATURAL PHILOSOPHY. 

In the case of the screw, equilibrium results when the 
circumference at which the force is applied bears the 
same proportion to the pitch of the screw, as the resist- 
ance bears to the applied force. 

Thus, if a copying-press has a screw of four threads to the 
inch, and the circumference at which the force is applied 
by the hands is thirty inches, then, disregarding the friction 
of the screw, a force of thirty pounds weight applied at the 
handle will produce a pressure on the copying-book of 
30 X 120 =" 3600 lbs. weight. 

150. The Endless Screw.— Fig. 47 is a contrivance 
for giving a slow motion to a wheel, to the axis of which 
a weight is attached. Moving 
the winch D B, the threads of 

the screw or ivorm a b c, act iliM^ - v - , =--\z«| 5 
on the cogs of the wheel, and 
raise the weight attached to 
the axle. 




D 



151. Compound Ma- 
chines. — No matter how 

. Fig. 47. Worm and w heel. 

great the complexity of a 

machine, it consists of various combinations of some or 
all of the simple machines, or mechanical powers, just de- 
scribed ; viz., of the lever, the pulley, the inclined plane, 
the wedge, and the screw. In all cases the advantage of the 
machine may be determined by calculating the effect of 
each simple machine separately and then combining the 
results. 

If, in any case, the distance through which the power 
and the weight move can be directly measured, then, 
disregarding friction, the power multiplied by the dis- 
tance through which it moves, will be equal to the weight 
multiplied by the distance through which it moves. 

152. Perpetual Motion. — Many persons, ignorant of 



PROBLEMS. 99 

the fact that machines do not create energy but only 
transmit the energy imparted to them, have vainly en- 
deavored to design a machine that, once set in motion, 
should not only continue to move forever afterwards, but 
should even give energy to other bodies, without losing 
any of its own energy. 

If a body could be set in motion in a place where it 
would be exposed to no friction nor fluid resistance, it 
would continue to move for ever. Such conditions, how- 
ever, are impossible ; and even if they did exist, such a 
| machine would be useless, since it would possess only a 
certain quantity of energy ; namely, the energy applied 
to start it; and if employed to impart motion to other 
machines, or to do any work, it would cease moving as 
soon as it had expended an amount of energy equal to 
that originally imparted to it. 

<K>a*Oc 

PR OB LEMS. 

1. A man lifts a hod of bricks weighing 50 lbs. through a ver- 
tical distance of 50 feet. What amount of work will he neces- 
sarily perform in the process, expressed in foot-pounds ? 

Arts. 2500 foot-pounds. 

2. A boy weighing 80 lbs. runs up a flight of stairs having a 
total difference of elevation of 100 feet. How much wort does 

! he expend in lifting his weight against gravitational force ? Ex- 
press result in foot-pounds. Ans. 8000 foot-pounds. 

3. If, in the last case considered, he ran up the stairs in thirty 
seconds, what would be his average activity, in foot-pounds-per- 
second ? Ans, 266.7 foot-pounds-per-second. 

4. A racing row-boat is propelled by eight oarsmen at a speed 
of 1000 feet per minute, and with an average force equal to 80 lbs. 
weight applied horizontally at the bow of the boat. What is the 
average activity of each oarsman in foot-pounds-per-minute ? 

Ans. 10.000 foot-pounds-per-minute. 



100 NATURAL PHILOSOPHY. 

5. The Atlantic liner " Paris " is stated to indicate 20,000 horse- 
power. Assuming that she steams across the Atlantic in six days, 
what total amount of work does she perform on the journey, in 
foot-pounds? Am. 5,702,400,000,000 foot-pounds. 

6. In a windlass such as shown in Fig. 38, page 93, the circum- 
ference described by the handle W y is six feet. The circumference 
of the axle on which the rope is wound is one foot. Then, disre- 
garding the weight and thickness of the rope, what weight can 
be raised by a force of thirty pounds' weight applied at TF? 

Arts. 180 lbs. weight. 

7. In a movable pulley such as shown in Fig. 40, page 95, what 
force at P, disregarding friction, will be required to raise 2240 lbs. 
at W? Arts. 1120 lbs. weight. 

8. What force would be required in the case of the compound 
pulley shown in Fig. 41, page 95, to be applied at P, to raise the 
same weight when hung at W1 Arts. 373.3 lbs. weight. 

9. The screw of a copying press has five threads to the inch. 
If the handle at which the power is applied moves through a cir- 
cumference of four feet, then, disregarding friction, what pressure 
will be exerted on the copying book by a force of 50 lbs. weight 
applied at the circumference ? Arts. 12,000 lbs. 




PART II 
Fluids. 



CHAPTER VIII. 

HYDROSTATICS. 

153. Fluids, or bodies that flow, are either liquids or 
gases. 

The phenomena of the rest and motion of fluids may 
be studied under the heads of 

(1.) Hydrostatics, which treats of liquids at rest. 

(2.) Hydraulics, which treats of liquids in motion. 

(3.) Pneumatics, which treats of gases either at rest or in 
motion. 

154. Compressibility of Liquids. — Liquids are but 
slightly compressible. Water, when subjected to a pres- 
sure of fifteen pounds to the square inch, is compressed 
only the 2Woo" °f its volume. Many other liquids are 
even less compressible. 

Liquids as a rule, however, are more compressible than solids. Usu- 
ally when solids are compressed, they are not confined at the sides. 
The particles, therefore, spread. Solids, therefore, appear to be more 
compressible than liquids. If, to prevent solids from spreading later- 
ally, we should confine them in strong vessels, as we must do with 
liquids, we should find solids to be less compressible than liquids. 

The molecules of liquids possess great freedom of mo- 

101 



102 



NATURAL PHILOSOPHY. 



tion ; they slip, slide, or move over one another with prac- 
tically no resistance. 

155. Pascal's Law of Transmission of Pressure. — 

Liquids transmit the pressure exerted on any part of their mass 
in all directions and without sensible loss of intensity. 

Liquids transmit pressure equally well in all directions 
because of the great freedom with which their molecules 
move in any direction over one another; moreover, liquids 
experience no loss in transmitting pressure from any part 
of their mass to any other part. 

The pressure due to the weight of a solid is exerted in one direction 
only ; viz., vertically downwards. A solid, therefore, may be in equilib- 
rium when supported on its base. The pressure due to the weight of a 
liquid is exerted in all directions. A liquid, therefore, to be in equi- 
librium, must be supported at the sides as well as at the base. 

156. Liquid Pressure as a Mechanical Power. — 

Since pressure is transmitted through liquids as well in 
one direction as in another, and without any sensible loss 
of intensity during the transmission, the total pressure sus- 
tained by any surface is proportional to its area. Liquid 
pressure, therefore, furnishes us with an additional me- 
chanical power. 

If, for example, two vessels, A and J?, Fig. 48, filled with 

water, be furnished with pis- 
tons, O and D ; that is, with 
parts arranged so as to move 
freely up and down the ves- 
sels, without allowing the wa- 
ter to pass them, and these 
vessels be connected by a tube 
T, we have a simple machine, 
or practically, a mechanical power, by which we can mod- 
ify the effect of a force to any desired extent. Suppose 
the areas of the two pistons C and Z), be respectively 1 
and 100 square inches. If the piston 0, be pushed down 



100 lbs. 



lib. 




Fig. 48.— Liquid Pressure as a Me- 
chanical Power. 



HYDROSTATICS. 



103 



with a force of one lb., the piston 7), will be raised with 
a force of 100 lbs. ; for, since a pressure of 1 lb. at (7, is 
exerted on the area of one square inch, it exerts a pressure 
of 1 lb. on every square inch ot surface in the two vessels. 
But the piston i), is the only other part of the vessel that 
can move, and, as it contains 100 square inches, it must 
be pushed upwards with a force of 100 lbs. 

As in any other machine, the work expended at the end where the 
force is applied, is equal to the work done at the end where the resist- 
ance is overcome. In the above case if the piston C, be moved through 
one foot, D, would be raised through the t £q ft. But 1 lb. x 1 ft. = I 
ft.-pound, and t ^q ft- x 100 lbs. = 1 ft.-pound. 

157. The Hydrostatic Press. — The machine just de= 
scribed forms what is known as the hydrostatic press. A 
lever P, Fig. 49, is attached 
to the piston A, and by its 
movement, oil or water is 
pumped into the larger 
vessel in which the piston 

B, moves. The pressure 
thus exerted causes the 
piston B, to rise. Sub- 
stances to be compressed, 
such as hay or cotton, are 
placed between a platform 

C, attached to the piston B, 
and a strong frame D, attached to the press. 

The hydrostatic press is employed in the arts for a variety of purposes 
where great pressure is required, such as raising heavy weights; ex- 
tracting oil from seed ; compressing hay or cotton ; moulding plastic 
material, like clay, in the manufacture of bricks, terra cotta, etc., and 
for many other purposes. 

158. Pressure Caused by the Weight of a Liquid. 

— Every molecule of a liquid has to bear the weight of all 
the molecules directly above it. The greater the depth of 




Fig. 49.— The Hydrostatic Press. 



104 



NATURAL PHILOSOPHY. 



the liquid, the greater the number of these molecules; 
therefore the pressure exerted by any liquid increases 
with the depth of the liquid. The pressure exerted by 
any liquid increases also with its density; for example, 
a vessel filled with mercury or with molasses, will have a 
greater pressure on its sides and base than if it were 
filled with water, because mercury or molasses is denser 
than water. 

As liquids exert pressure equally well in all direc- 
tions, the downward, upward, and lateral pressures at 
any point within the liquid must balance one an- 
other. 

159. The Downward Pressure or the Pressure on 
the Base. — The pressure on the horizontal base of a ves- 
sel filled with liquid depends only on the area of the base 
and the depth of the liquid. The amount of this pressure 
may be greater than, equal to, or less than the weight of 
liquid in the vessel. 

If the vessel has vertical walls as at A, Fig. 50, the pres- 






Fig. 50.— The Pressure on the Base. 

sure on its base will be exactly equal to the weight of the 
liquid in the vessel ; if the walls are inclined as at B, the 
pressure on the base is the same as at A, and is greater 
than the weight of the contained liquid ; if the walls are 
inclined as at 0, the pressure on the base is the same 
as at A, and is less than the weight of the contained 
liquid. 



HYDROSTATICS. 105 

It might be supposed that the total pressure on the base of any vessel 
would always equal the weight of the liquid in the vessel ; but in the 
vessel B, the particles at the surface not only transmit their pressure to 
those parts of the base directly under them, but also to all parts of the 
base c' d / '. The total pressure on the base, therefore, is the same as if 
there was the same depth of liquid over all parts of the base as there is 
over the middle parts ; that is, the total pressure is equal to the weight 
of the column of water, a / b' c / d' . In the vessel C, only the particles 
of the liquid immediately above the base exert a pressure on the base ; 
the inclined walls receive the pressure of the remaining particles. 

If, therefore, different vessels having horizontal bases of the same 
area, are filled to the same depth with water, the pressure on the base 
of each vessel will be the same, although the shape of the vessels and 
the quantity and weight of water in the vessels may differ. The prin- 
ciple that the pressure on the base of a vessel does not depend upon its 
shape and capacity is known as the hydrostatic paradox. 

160. Total Pressure Expressed as Weight. — In cal- 
culating the pressure produced by the weight of any liquid 
in a containing vessel, it is convenient to express such 
pressure as equal to the weight of so many cubic inches 
or cubic centimetres of water. 

The total pressure on the base of a vessel containing 
any liquid, is equal to the weight of a column of liquid 
whose base is that of the vessel, and whose height is 
equal to the vertical distance from the middle of the base 
to the surface of the liquid. 

Pressures are commonly expressed by the height of the liquid in the 
containing vessel above the point considered. Thus we frequently speak 
of a pressure of, say 3 inches of water, meaning the total pressure of a 
column of water 3 inches high on an area of one square inch. 

To calculate the total pressure in pounds weight on a horizontal base, 
multiply the area of the base in square inches by the depth of the water 
in inches, and the product by the weight of a cubic inch of water; i. e., 
0.03612 lb. Thus a bucket with a base 50 sq. in. in area, filled with 
water to a depth of 10 inches, supports on its base a total pressure of 
50 x 10 x 0.03612 = 18.06 lbs. weight. The use of the French system 
of weights and measures greatly simplifies such calculations, for the 
area of the base in sq. cms. multiplied by the depth in cms. gives at 



106 NATURAL PHILOSOPHY. 

once the total pressure in grammes weight, since 1 c. c. of water weighs 
one gramme. Thus, in the preceding case, 50 sq. in. = 322. 6 sq. cms. 
and 10 in. = 25.4 cms., so that the total pressure on the base of the 
bucket = 322.6 x 25.4 = 8192 grammes weight = 18.06 lbs. 

161. Pressure on the Sides of a Vessel. — The pres- 
sure on any vertical side of a vessel containing liquid, is 
equal to the weight of a volume of the liquid, obtained by 
multiplying the area of that side by the vertical distance 
from the centre of gravity of the side to the surface of the 
liquid. 

In a rectangular vessel filled with water, the centre of gravity of the 
side will be at its geometrical centre ; i. e., at the intersection of diag- 
onals drawn from opposite corners, or half way up the side. 

A rectangular vessel 3 feet long, 2 feet wide, and 1 foot deep (91.44 
cms. long, 60.96 cms. wide, and 30.48 cms. deep), when filled with 
water, has exerted on each of its longer sides a total pressure equal to 
the weight of 3 feet of water ; for the area of each of these sides is 3 x 
2 = 6 sq. ft., which multiplied by half the height = 3 cubic feet. Since 
one cubic foot of water = 62.4 lbs., the total pressure is 62.4 x 3 = 187.2 
lbs. (91.44 cms. x 60.96 = 5,574.2 sq. cms. x 15.24 = 84.951 cub. cms. 
or grammes = 187.2 lbs.). 

162. Upward Pressure. — The upward pressure in 
pounds weight at any surface in a liquid is equal to the 
downward pressure at that surface, and is, therefore, equal 
to the area of the surface, multiplied by its depth below 
the surface of the liquid, multiplied by the weight of one 
cubic inch of water. Or, expressed in grammes weight, 
the pressure is equal to the area in sq. cms. multiplied by 
the depth in cms. 

The area of the base cd, Fig. 51, is one square inch (6.45 sq. cms.), 
and the water over it is 12 inches (30.48 cms.) deep. Then the upward 
pressure is 1 x 12 x .036 = .432 lb. avoir. The quantity .036 is the 
weight of a cubic inch of water. Or, 6.45 sq. cms. x 30.48 cms. x 1 
gramme = 196.6 grammes = .432 lb. 

Experiment 32. — Procure a glass chimney B, Fig. 51, with straight 



HYDROSTATICS. 



107 



sides and smooth ends. Cut a disc c d, of mica, such as is used for the 

doors of stoves, large enough to cover the base of the 

chimney. Attach a string to the middle of the disc. 

Now, placing the disc so as to cover one end of the 

chimney, and holding the disc against the end by the 

string, push the chimney vertically downwards into a 

vessel A, filled with water. Observe that after some 

little depth has been reached, the string need no longer 

be held, as the total upward pressure, caused by the 

water in A, endeavoring to flow into B, will hold the 

disc in its place. 




Fig. 51.— Upward 
Pressure, 



To find the amount of this total upward pressure, 
pour water into the chimney, or let the water gradu- 
ally leak into the chimney at the base until the disc 
falls off, which will take place when the level of the 
water in the chimney is the same as on the outside. At this moment 
the total downward pressure, caused by the water in J5, is equal to the 
total upward pressure, caused by the water in A. Since the sides of 
the chimney are vertical, the total downward pressure is equal to the 
weight of the water in B ; hence the total upward pressure on c d , is 
equal to the weight of a column of water whose base is c d, and whose 
height is the depth of the liquid above c d. 

163. Surface of Liquids at Rest. — When a liquid is 
at rest, its upper surface is level or horizontal ; for, were it 
higher at one point than another, the greater pressure so 
produced would press it up at the lower points until the 
entire surface became level. 

It is the surface of a comparatively small extent of 
water only that may be regarded as horizontal. Large 
water surfaces, like those of the ocean, are curved. For 
any mass of water to be in equilibrium, all parts of its free 
surface must be at equal distances from the earth's centre. 

164. Equilibrium of Liquids in Communicating 
Vessels. — A liquid placed in communicating vessels is 
in equilibrium when its level stands at the same height 
in all the vessels ; for, were it higher in one vessel than 
in the others, the greater pressure so produced in the 
highest vessel would cause the liquid to mount in the 



108 



NATURAL PHILOSOPHY. 



other vessels until it stood at the same height in all. 
Water rises from the pipes in the streets o( a city, and 
(ills the pipes in the houses, because the level o( water 
in the basin or reservoir in which it is stored, is equal to 
or greater than the height of the houses. 

As we bave already soon, liquids in capillary tubes form an exception 
to this statement, the Level being higher when the liquid wets the walls 
of the tubes, and lower when it does not wet them. 

In artesian wells, water is forced up from great depths 
by the pressure of water contained between two curved 
impervious or water-tight strata. Fig. 52 shows a section 




Fig, 52— An Artesian Well, 



of an artesian well. The liquid is forced up through the 
well, and caused to escape at the surface, by reason of the 
pressure of the liquid at a higher level, contained between 
the impervious strata. 

Two liquids o( different densities placed in communi- 
cating vessels will be in equilibrium when the level of the 
denser liquid is as much lower than the level o( the lighter 
liquid as the density of the former is greater than the dens- 
ity of the latter. In other words the heights of liquid col- 



HYDROSTATICS. 



109 




umns of different densities in communicating vessels are 
inversely as the densities. 

165. Archimedes' Principle. Buoyancy. — Bodies 
immersed in a liquid weigh less than in air, losing an 
amount of weight equal to the weight of the liquid they 
displace. This important principle was discovered by 
Archimedes. 

Suppose the cube abed, Fig. 53, be completely im- 
mersed in water. Consider the manner in which the 
pressures exerted on its surfaces by 
the liquid affect the weight of the 
cube. The pressures on the opposite 
vertical sides, being equal, will neu- 
tralize each other. The downward 
pressure, on the top, is equal to the 
weight of a column whose base is 
equal to the top of the cube, and 
whose height is the depth of the 
liquid e d, at this surface ; the up- 
ward pressure on the base is equal to the weight of a 
column of liquid whose base is equal to the bottom of 
the cube, and whose height is e c. The upward pressure, 
therefore, exceeds the downward pressure, by a weight of 
water equal to the weight of the volume of the cube. 

This excess of upward pressure, being exerted in a direc- 
tion opposite to that of the force of gravity, will cause the 
cube to lose an amount of weight equal to the weight of 
the water it displaces ; this loss of weight is due to the 
excess of the upward pressure over the downward pres- 
sure and is called buoyancy. 

166. Experimental Proof of the Principle of Ar- 
chimedes. — The correctness of the principle of Archi- 
medes may be demonstrated by means of the apparatus 
shown in Fig. 54. A closed cylinder B, of such a size 
as exactly to fill the hollow cylinder A, is suspended 

K 



Fig, 53.— Canse of Buoy- 
ancy, 



110 



NATURAL PHILOSOPHY. 




Fig. 54, Principle of 
Archimedes. 



below it, the two attached to the pan of a balance, and 

counterpoised in air by weights at 0. The cylinder 
B, is then completely immersed in 
water, as shown in the figure. The 
buoyancy of the water on the cylin- 
der B, causes it to lose weight, as is 
shown by the other pan of the bal- 
ance falling. If now, the cylinder 
A, be exactly filled with water, equi- 
librium will be restored. The weight 
lost by B, therefore, is equal to the 
weight of a volume of water which 
will just fill A ; but this volume is 
the same as that displaced by B; 

therefore, the weight lost by J5, is equal to the weight of 

the water it displaces. 

167. Floating Bodies. — A body placed in a liquid will 
float if it displaces a bulk of liquid equal to its weight; 
because the buoyancy of the liquid, which holds the 
body up, is equal to the force of gravity, which pulls it 
down. 

Buoyancy acts at a point called the centre of buoyancy, 
which is the centre of gravity of the displaced liquid. 

168. Elements of the Force of Buoyancy. — 

(1.) The point of application of the force of buoyancy 
is at the centre of buoyancy. 

(2.) The direction of buoyancy is vertically upwards. 

(3.) The intensity of buoyancy is equal to the weight 
of the liquid displaced. 

169. Equilibrium of Floating Bodies. — In order that 
a body may float, the force of buoyancy must equal the 
force of gravity. In order that a floating body may be in 
equilibrium, the centres of gravity and of buoyancy must 
be in the same vertical line. Thus, in Fig. 55, the boat A, is 
in equilibrium, since the forces of gravity and of buoyancy 



HYDROSTATICS. 



Ill 




acting at G and 0, respectively , are opposed, and equal to 
each other ; but, if the 
the boat be moved into 
the position represented 
in B, it is no longer in 
equilibrium, since grav- 
ity and buoyancy are 

no longer directly Op- Fig ' ^"Equilibrium of Floating Bodies. 

posed to each other, but tend to turn the boat around, 
until they are both in the same vertical line. 

There are three varieties of equilibrium in a floating 
body: 

(1.) Stable Equilibrium, in which the centre of buoyancy 
is either above the centre of gravity, or, in which the centre 
of gravity is as low as it can get, as in Fig. 56, where the 




K » 

f\ / 

\ / 




_ .- . 


1 1 


jjjjl 


H 




Fig, 56,— Stable Equilibrium, 



Fig. 57— Unstable 
Equilibrium, 



Fig. 58— Neutral 
Equilibrium. 



centre of gravity G, is as low as it can be in any position 
of the body. 

(2.) Unstable Equilibrium, in which the centre of buoy- 
ancy B, is below the centre of gravity G, as in Fig. 57. 

(3.) Neutral Equilibrium, in which the relative positions 
of the centres of gravity and buoyancy are not affected by 
any movement of the body. A sphere floating on water, 
as shown in Fig. 58, is in neutral equilibrium. 

In the above examples, it will be noticed that the centre 
of buoyancy acts as the point of support of the floating 
body, and bears the same relation to the centre of gravity 



112 NATURAL PHILOSOPHY. 

as does the point of support of bodies capable of moving 
freely on an axis, as will be seen by comparing Fig. 57 
with Fig. 13. A floating sphere entirely submerged would 
be in neutral equilibrium, and would then compare with 
Fig. 14. 

The equilibrium of a boat or ship is more nearly stable 
as its centre of gravity is lower. When a ship is not 
heavily laden, ballast is put in the lower part of the 
vessel in order to lower the centre of gravity. 

170. Specific Gravity. — A pint of mercury weighs 13.6 
times as much as a pint of water. In other words, if we 
compare the weights of equal bulks of mercury and water, 
we shall find that the mercury is 13.6 times heavier than 
the water. This number 13.6 is called the specific gravity 
of mercury, and represents the specific or particular effect 
of gravity on a given volume of mercury, as compared 
with its effect on an equal volume of water. 

A pound of mercury occupies a bulk 13.6 times less 
than that occupied by a pound of water. That is, gravity 
produces the same effect of weight on a given volume of 
mercury that it does in a volume of water 13.6 times 
greater ; or, as before, the specific gravity of mercury is 
13.6 times as great as that of water. 

171. General Methods of Determining Specific 
Gravity. — There are two general methods for determin- 
ing the specific gravity of a substance: 

(1.) By the comparison of the weights of equal vol- 
umes. 

(2.) By the comparison of the volumes of equal weights. 

The specific gravity of solids and liquids is generally 
referred to pure water as a standard. That of gases and 
vapors is generally referred to air. 

The specific gravity of a substance may be determined 
by a comparison of the weights of equal volumes of the 
substance and water as follows: 



HYDROSTATICS. 113 

Rule. Divide the weight of the body in air by the weight of 
an equal volume of water. 
This may be expressed as follows ; viz., 




n W _ Weight of body in air. 

^' ' W / Weight of equal bulk of water. 




Fig. 59.— A General Formula for Specific Gravity. 

The specific gravity of a gas is determined in the same 

manner, air, instead of water, being taken as the standard 

of reference. 

In order, therefore, to determine the specific gravity of any 

\ body, it is only necessary to ascertain the weight of that body 

and the weight of an equal balk of water or of air. 

Suppose, for example, it is required to determine the 
specific gravity of a piece of iron. First find the weight 
i of the iron in air, which we will suppose to be 7780 
grammes. Then find the weight of an equal bulk of 
water, which will be, say, 1000 grammes. The specific 
gravity of the iron, therefore, is J g g g = 7.78 ; or, in other 
words, the iron is 7.78 times heavier than water. 

When great accuracy is desired the weights of the body and the equal 
bulk of water are taken in vacuo. 

172. Methods of Obtaining Specific Gravity by the 
Balance, for Solids Heavier than Water. — Since a 
1 body immersed in water loses as much weight as the weight 
of the water it displaces, it is easy to obtain its specific grav- 
ity by the balance ; for, attach the body to a string tied to one 
of the pans of a balance ; exactly balance the body by add- 
ing weights to the other pan ; these weights will give the 
weight W, of the solid in air. Then, while still attached 
to the balance, immerse the solid in water, and find the 
weight it loses. This weight will give W, the weight of 
a bulk of water equal to that of the solid. Then W, 



114 NATURAL PHILOSOPHY. 

divided by W\ will give the specific gravity of the sub- 
stance. Suppose, for example, a solid weighs in air 2000 
grammes, and loses in water 1500 grammes, then its spe- 
cific gravity = $$$% = i- 333 - 

173. Balance Method for Solids Lighter than 
Water. — Attach the body, i. e., such as a piece of cork, 
to a solid, say a piece of copper, heavy enough to sink 
the cork in the water. Find the weight which the two 
lose when immersed in water. Find what weight the 
copper loses when immersed in water ; then the difference 
in this weight and the weight that both lose in water, will 
give the weight which the cork loses in water. Divide the 
weight of the cork in air, by the weight it loses in water, 
and the quotient will be the specific gravity. Suppose, 
for example, the cork weighs 6 grammes, and that, when 
both are immersed in water they lose 100 grammes, also 
that the heavier solid, when immersed in water, loses 10 
grammes. The cork must lose 90 grammes, and its specific 
gravity must equal f$ or 0.667. 

174. Balance Method for Liquids. — A closed bulb 
D, Fig. 60, partly filled with mercury, or other substance 

sufficiently dense to sink it in most liquids, is 
attached to a string, and suspended from one of 
the pans of a balance. First find the weight 
which the bulb loses when immersed in the 
liquid whose specific gravity is desired. This 
will be the weight of a volume of liquid equal 

4 to the volume of the bulb D; then find the 
weight which the bulb D, loses when immersed 
in water ; this will give the weight of the volume 
Fi 60 — °f water equal to that of the bulb. Then divide 
Specific- the weight the bulb loses in the liquid whose spe- 
Gravity c ^ c g rav jty is desired, by the weight it loses in 
water, and the quotient will be the specific gravity. 
Suppose, for example, the bulb D, loses 1840 grammes 



I 



HYDR OSTA TICS. 115 

when immersed in sulphuric acid, and 1000 grammes when 
immersed in water; then yffo" = 1-84, the specific gravity 
of the sulphuric acid. 

175. By the Specific-Gravity Bottle. — The specific 
gravity of a liquid may be conveniently found by means 
of a bottle, which is first weighed when empty, and then 
filled with the liquid, say milk, whose specific gravity is 
desired, and again weighed ; this weight, less the weight 
of the bottle, will give the weight of a quantity of milk, 
that will exactly fill the bottle ; the bottle is then emptied, 
filled with water, and again weighed. This weight, less 
the weight of the bottle, will give the weight of the water 
that will exactly fill the bottle; then the w T eight of the 
milk, divided by the weight of the water, will give the 
specific gravity of the milk. 

Thus, suppose the bottle, when empty, weighs 300 grammes, when 
filled with milk, 1326 grammes, and when filled with water, 1300 
grammes; then 1326 — 300 = 1026 grammes, the weight of the milk, 
and 1 300 — 300 = 1000 grammes, the weight of the water, and ^gff = 
1.026, the specific gravity of the milk. 

176. By the Hydrometer. — A pound of water occu- 
pies a space 13.6 times greater than a pound of mercury ; 
that is, if we compare the weights of equal volumes of 
mercury and of water we shall find that the mercury 
occupies a space or volume 13.6 times smaller than the 
water. This number 13.6 is called the specific gravity 
of mercury. 

The specific gravity of a liquid may be determined by 
the comparison of the volumes of equal weights by means 
of the following 

Rule. — Divide the volume of a given weight of water by the 
volume of an equal weight of the substance whose specific gravity 
is required. 

Or, 

o p V' _ Volume of the water. 

' V Volume of the liquid. 



116 



NATURAL PHILOSOPHY. 




The apparatus generally employed for this purpose is 
called a hydrometer. 

One form of hydrometer is seen in Fig. 61. It is made 
of glass and is hollow except at its lower end, which con- 
tains sufficient mercury, or other heavy sub- 
stance, to cause it to float upright when 
placed in any ordinary liquid. When the 
instrument is placed in any liquid, it will 
sink until it displaces a bulk of liquid equal 
in weight to its own weight. But, the denser 
the liquid, the less the depth to which the 
hydrometer will sink ; for the less will be 
the bulk of liquid required to equal in 
weight the weight of the instrument. 

The specific gravity of any liquid may, 
therefore, be determined by comparing the 
distance to which the instrument sinks when placed in 
water, with the distance it sinks when placed in the 
liquid whose specific gravity is desired. A scale, marked 
on the tube, usually gives the specific gravity by direct 
inspection. 

Instruments of this kind, when used to determine the 
specific gravity of milk, are called lactometers; and of 
alcohol, alcoholometers} 

1 In the following table, the specific gravity of a few common sub- 
stances will be found. It should, however, be remembered that the 
specific gravities vary slightly with different specimens of the same sub- 
stance. 






Fig. 61 -Hy- 
drometer. 



Solids. 




Ice 


= 


.87 


Iron 


= 


7.78 


Cork 


= 


.24 


Zinc 


= 


7.19 


Liquids. 




Lead 


= 


11.35 


Mercury 


= 


13.595 


Copper 


= 


8.90 


Sulphuric Acid 


= 


1.84 


Silver 


= 


10.47 


Milk 


= 


1.026 


Gold 


= 


19.30 


Ocean Water 


= 


1.026 


Platinum 


= 


22.06 


Alcohol 


= 


.792 


Granite 


= 


2.75 


Ether 


= 


.715 



PROBLEMS. 117 

Since the weight of a cubic foot of water = 62.4 lbs. avoir., if we 
know the specific gravity of any substance, we can easily calculate the 
weight of a cubic foot of that substance ; thus, the sp. gr. of gold = 
19.30; then a cubic foot of gold - 19.30 x 62.4 = 1204.32 lbs. So 
also, if we know the weight of a body and its specific gravity, we can 
calculate its volume. Thus, What is the volume of 100 lbs. of gold ? 
Since one cubic foot of gold has a weight of 1204.32 lbs., 100 lbs. must 

occupy the . 9f> , ~~ of a cubic foot = 0.08303 cubic foot. 

Again, since one cubic centimetre of water equals one gramme, the 
weight in grammes of one c. c. of any substance will be equal to its spe- 
cific gravity ; thus, the weight of one c. c. of mercury is 13,595 grammes. 



Problems. 

1. A reservoir is filled with water to a depth of 50 feet. What 
is the pressure, in lbs. per square inch and in grammes per square 
centimetre, on the bottom of the reservoir, in excess of the pressure 
of the atmosphere? Arts. 21.67 lbs. per sq. in. 

1524 gms. per sq. cm. 

2. The Pacific Ocean is in some places 4000 fathoms ; i. e., 24,000 
feet deep. What is the pressure at the bottom in excess of the 
pressure of the atmosphere, in lbs. per square inch and in grammes 
per square centimetre. Arts. 10,400 lbs. per sq. in. 

731 ,520 gms. per sq. cm. 

3. In the case of the last example, suppose a corked empty glass 
bottle to be so loaded as to sink to the bottom of the ocean. If 
the neck of the bottle has an internal cross-sectional area of 3 
square centimetres, what will be the total pressure on the cork 
tending to drive it into the bottle, in pounds weight and in 
kilogrammes weight? Ans. 4838 lbs. weight. 

2,194.560 kilogrammes weight. 

4. An empty tumbler has 100 cubic centimeters of ice placed 
in it, and is then completely filled with water, so that the tumbler 
is not only full to the brim, but the floating ice projects above the 



118 NATURAL PHILOSOPHY. 

surface. When the ice has all melted, how much water will have 
overflowed from the tumbler? and why? Arts. None. Because 
the ice displaces its own weight of water, and, therefore, its own 
volume of water when melted. 

5. A log of wood has a volume of 100,000 cubic centimetres, 
and weighs 70 kilogrammes. How much weight in lbs. and in 
grammes will be required to just sink the log in fresh water? 

Am. 66.14 lbs. 

30,000 grammes. 

6. A loaded boat weighing in air 20 tons of 2240 lbs. is floated 
in fresh water. How much water in lbs. weight, in cubic feet, and 
in cubic centimetres will it displace ? 

Arts. 44,809 lbs. 

717.9 cubic feet. 

20,321,000 cubic centimetres. 

7. If the same loaded boat be floated in sea water of specific 
gravity 1.026, how much water will it displace in lbs. weight, in 
cubic feet, and in cubic centimetres ? 

A?is. 44,800 lbs. 

699.7 cubic feet. 

19,806,000 cubic centimetres. 

8. A stone has a volume of 80,000 cubic centimetres and has a 
mass of 240 kilogrammes. What is its specific gravity ? 

Arts. 3. 

9. The standard pressure of the atmosphere at sea level is usu- 
ally considered as being equal to that of a column of pure mer- 
cury at 0° C, 760 millimetres in height. Taking the specific 
gravity of mercury as 13.595, what would be the height in feet 
and in centimetres of the corresponding column of pure water? 

Arts. 33.99 feet. 
1,033.2 cms. 

10. A specimen of metal weighs 120 grammes in air, and 106.5 
grammes in water. What is the specific gravity of the specimen, 
and of what metal is it probably composed ? 

Ans. 8.89. Copper. 




CHAPTER IX. 



HYDRAULICS. 



177. Hydraulics treats of liquids in motion. It de- 
scribes the flow and elevation of liquids, and the machines 
for moving liquids, or intended to be moved by them. 

178. Escape of Liquid from Orifices in Containing 
Vessels. — The walls of a vessel filled with liquids are sub- 
jected to two pressures : 

(1.) The pressure of the liquid directed outwards, from 
within. 

(2.) The pressure of the air directed inwards, from 
without. 

If a hole be pierced in a side of a vessel containing a liquid, the 
liquid will escape only when the pressure from within is greater than 
the atmospheric pressure. If the vessel be open at the top, so as to per- 
mit the pressure of the air to act on the upper surface of the liquid, the 
liquid is pushed out of the orifice, by the pressure of the air, with the same 
force as that with which it is pressed in. The liquid, therefore, tends to 
run out with a force equal to the pressure caused by the depth of the 
liquid above the opening ; or, in other words, the effect of atmospheric 
pressure is eliminated. 

Water flowing from a narrow-necked bottle does not es- 
cape in a steady stream, but, at more or less regular in- 
tervals partially stops flowing, until a few bubbles of air 

119 



120 



NATURAL PHILOSOPHY. 



enter the neck of the bottle with a gurgling sound, when 
the flow again begins. The partial stoppages are due to 
the pressure of the atmosphere, which occasionally forces 
bubbles of air into the bottle against the pressure of the 
escaping liquid. The air thus forced into the bottle occu- 
pies the space left by the liquid which has escaped. After 
a certain quantity of the liquid has escaped, the pressure 
of the air against the mouth of the bottle becomes greater 
than the pressure forcing the liquid out. More air then 
enters, and more liquid escapes. Were a hole made in the 
bottom of the bottle, the liquid would escape in a steady 
stream. 

179. Theorem of Torricelli. — If an opening or orifice 
be made at the middle point c, of a vessel filled with water, 
and also at a, 6, d and e, at equal distances above and below 

c, and the water be permitted 
to escape in a horizontal di- 
rection ; then the greater the 
distance of the orifice below 
the surface of the water, the 
greater will be the velocity 
with which the water will 
flow from the vessel. 

If an opening provided 
with a vertical jet be made 
at j\ exactly opposite e, then 
the velocity with which the 
water escapes at j, may be determined by the height 
reached by the jet. This may be taken as approximately 
the vertical distance j A ; for, disregarding the resistance 
of the air, the initial velocity of a body thrown upwards 
to a given vertical distance is equal to the velocity the 
body would acquire in freely falling through that distance. 
Therefore, the water escapes at j, with the same velocity it 
would acquire in falling through the vertical distance jA, 
called the head. 




Fig. 62.— Torricelli's Vase. 



HYDRAULICS, 121 

But the velocity in feet per second, acquired by a body 
falling through a given distance is equal, approximately, 
to eight times the square root of that distance in feet 
(more nearly 8.02). Or, since this distance is the head, 
the velocity in feet per second, will be 8.02 multiplied by 
the square root of the head in feet. 

This principle was discovered by an Italian philosopher 
named Torricelli, and is generally known as Torricelli's 
Theorem. 

Torricelli 's theorem may be expressed as follows : 

Liquids flow from an orifice in a containing vessel with the 
velocity they would acquire in falling freely from the level of the 
liquid to the centre of gravity of the orifice. 

Suppose, for example, that the orifice was four feet 
below the surface of the liquid; then the velocity of 
escape would be 8.02 X i/I = 8.02 X 2 = 16.04 feet per 
second. 

180. Method of Ascertaining the Flow. — 

Experiment 33. — Bore three small holes of the same size in the 
side of a tin can, one near the bottom, one near the top, and the third 
midway between the two. Fill the can with water and note the quan- 
tity that escapes in the same time from each of the three openings. Ob- 
serve that the flow from the lowest hole is greatest and that from the 
upper hole is least. In order to avoid the effects produced by change 
of level, keep the can filled with water by pouring in water from time to 
time. 

The flow, or amount of liquid escaping from an orifice 
in a given time, may be ascertained by multiplying the 
velocity in feet-per-second with which the water comes 
out of the orifice, by the area of the orifice in decimals 
of a square foot, and by the number of seconds it contin- 
ues to flow. Since the velocity obtained from the preced- 
ing formula will be expressed in feet-per-second, if the 
area of the orifice is in square inches, the velocity must 
first be reduced to inches ; multiplying this by the time 
in seconds, will give the flow in cubic inches. 



122 NATURAL PHILOSOPHY. 

Similarly, if the velocity is expressed in centimetres per 
second, this velocity multipled by the area of the orifice in 
square centimetres and by the time, will give the flow in 
grammes, or in cubic centimetres. 

The area of the orifice multiplied by the velocity must give the rate 
of flow ; for, if the area of the orifice is one square inch, and the velo- 
city of the escape twelve inches per second ; then, in one second, a 
mass of water one inch in area of cross section and twelve inches long 
would flow out of the orifice, the volume of which would of course be 
twelve cubic inches. Since the velocity of escape from any vessel varies 
with^the head of the liquid, and this decreases as the liquid runs out, the 
quantity discharged from any given orifice must be greater during the 
first second than during the second, and greater during the second second 
than during the third, and so on. We cannot, therefore, ascertain the 
quantity discharged in, say 60 seconds, by multiplying the quantity dis- 
charged during the first second by 60, unless the head is kept constant 
by allowing water to run into the vessel as fast as it runs out. 

The actual flow is smaller than the theoretical velocity of escape mul- 
tiplied by the area of the orifice and the time ; because, 

(1.) Only the particles in the centre of the orifice acquire the theo- 
retical velocity. 

(2.) The particles surrounding the orifice on all sides produce cross 
currents and cause a contraction of the issuing stream. 

By adding small conical or cylindrical tubes, called adjutages, to the 
orifice, the actual flow can be made very nearly equal to the calculated 
flow, provided the liquid wets the walls of the tube. 

181. The Flow of Liquids through Horizontal 
Pipes. — When a liquid flows through long pipes, such as 
the water pipes of a city, the friction of the water against 
the sides of the pipes greatly diminishes the velocity of 
flow. This is especially the case at the bends of the pipe, 
where the liquid is forced suddenly to change the direction 
of its motion. It is on account of this decrease in velo- 
city, that water must be put under considerable pressure 
to cause a sufficient volume of liquid to flow through long 
pipes in a given time. 

182. Lateral Pressure. — A liquid in motion through a pipe exerts 
a much smaller pressure on its walls than when at rest. In the case of 



HYDRAULICS. 123 

a liquid falling through a vertical pipe, there is but little lateral pres- 
sure. The liquid does not touch the walls of the pipe, but is surrounded 
by a film of air, which adheres to it, and is dragged down in its flow. 
Air pumps employing mercury instead of water have been devised on 
this principle. Such pumps are commonly known as mercury pumps, 
and are employed to obtain a high vacuum in the chamber of incandes- 
cent electric lamps. 

183. The Velocity of Rivers.— The velocity of the 
water in a river depends, 

(1.) On the inclination of the bed or channel, that is, on 
the difference of level between its source and its mouth. 
This difference of level is the head under which the water 
escapes, but the actual velocity of the river is very much 
less than that the water would acquire in flowing freely 
under such a head, by reason of the friction against the 
air and the channel of the river. 

(2.) On the volume of water in the river; the greater the 
volume the greater the velocity. 

The velocity of the water at the surface is somewhat 
less than at some distance below the 
surface. The surface velocity of ordi- 
nary navigable rivers varies from about 
two to four miles per hour. 

184. Vertical Jets. — A jet of water 
escaping vertically upwards from a res- 
ervoir, does not actually rise as high 
as the level of the water in the reser- 
voir, because, 

(1.) Its velocity is diminished by 
,.\/ . ,* ., .., .„ J Fig. 63 -Height of Jet. 

friction against the sides of the orifice. 

(2.) Some of its motion is lost in pushing the air out of 
the way. 

(3.) The falling water strikes the water which is rising, 
and so decreases its velocity. 

185. Reaction of an Escaping Jet. — When a jet of 
liquid is escaping from an orifice in a vessel, it will pro- 




124 



NATURAL PHILOSOPHY. 




Fig, 64,— Eeaction Vase, 



duce a pressure, which, if the vessel is free to move, will 
cause it to move in a direction opposite to that in which 
the liquid is escaping. Suppose, for example, the vessel 
A, Fig. 64, has, at its lower end, a horizontal tube (7, the 

ends of which are bent as 
shown. As the liquid escapes 
from openings at the extremi- 
ties of this tube, the vessel ro- 
tates in a direction opposite to 
that in which the liquid is es- 
caping. 

The cause is as follows : Were the 
openings at the ends of the tube 
closed, the pressures on directly oppo- 
site portions of the wall being equal and 
opposite would neutralize each other. 
But when the liquid begins to run out of 
an opening, the pressure at this point 
is removed, and the pressure on the opposite side, being no longer neu- 
tralized, moves the vessel around. The direction in which this pressure 
acts is shown at D. This effect produced by the escaping liquid is called 
the reaction of the escaping jet. 

The amount of the pressure produced by the reaction of the escaping 
jet is equal to twice the pressure on the orifice produced by the liquid 
when at rest. 

186. Water- Wheels. — The moving water in a river 
represents a considerable amount of energy. We may- 
utilize this energy and cause it to do useful work ; i. e., to 
act as a water power, by permitting the moving water to 
impart its motion to a water-wheel. 

The commercial applications of water power are rapidly increasing. 
Now that the developments of electricity have rendered the transmis- 
sion of power more economical, the utilization of the energy of rivers is 
becoming quite common. Of the enormous energy of the Niagara River 
at Niagara Falls (about 7,000,000 horse-power), a part is already being 
utilized by electrical transmission. 

187. Energy Transferred from Running Water to 
Wheels. — There are three ways in which the energy of 



HYDRAULICS. 125 

motion of a running stream may be transferred to a water- 
wheel. 

(1.) By impact. The moving water is caused to strike float 
boards or buckets placed on the wheel and so to drive it. 

(2.) By weight. The wheel is provided with buckets 
so shaped as to hold the water as far as possible on one- 
half of the vertical diameter, and thus, by making that 
side heavier than the other, to drive the wheel. 

(3.) By the reaction of the escaping jet. The buckets are 
so shaped as best to permit the force of the escaping jet 
to drive the wheel. 

188. Direction of Greatest Efficiency of Driving 
Force. — The direction of greatest efficiency in which to 
apply the driving force of a running stream, whether this 
force be the force of impact, of weight, or of reaction, is 
in a direction at right angles to the diameter of the wheel, 
or tangential to its circumference. 

189. The Undershot- Wheel. — In the undershot water- 
wheel, the water strikes near the bottom of the wheel, against 
a number of flat boards called float-boards, placed as shown 
in Fig. 65. This wheel is moved mainly by the impact or 




Fig. 65— The Undershot* Wheel. 

blow produced by the moving water striking the float- 
boards. 

If the stream is a tidal one, so that the water sometimes flows in one 



126 



NATURAL PHILOSOPHY. 



direction and sometimes in another, the float-boards are usually placed 
at right angles to the rim of the wheel ; when, however, the direction 
of the stream is constant, the float-boards are inclined at an acute angle 
to the current, in which case the water acts partly by its weight. 

190. The Overshot- Wheel. — In the overshot-wheel 
the water is received at the top of the wheel by buckets, 
shaped as shown in Fig. 66, so as to retain a large propor- 




Pig. 66— The Overshot- Wheel. 

tion of the water until it reaches the lowest point. The 
wheel is moved by the momentum of the moving water 
and by the weight of the water in the buckets, that side 
of the wheel which receives the water, being heavier than 
the opposite side. 

The curvature given to the buckets is such as to meet most nearly the 
double requirement of their receiving the blow nearly at right angles to 
the radius of the wheel, and of retaining the water to as low a point on 
the wheel as possible. 

The overshot-wheel is applicable to cases where the amount of water 
is small, but the velocity great. The undershot-wheel is used when the 
quantity of water is great, and its velocity is comparatively small. 

191. The Breast- Wheel. — In the breast-wheel the wa- 
ter is received on the wheel at or near the level of the axis 
A, as shown in Fig. 67. The buckets are placed perpen- 
dicularly to the circumference of the wheel, and are 
arranged so as to hold the water until they reach the 



HYDRA ULICS. 



127 



lower point, which is done by causing the ends of the 
buckets to move near the curved waterway down which 
the water runs. The breast-wheel is turned both by the 
impact and the weight of the water. 




Fig. 67-The Breast-Wheel, 

The breast-wheel is an economical form of water-wheel, and is espe- 
cially applicable to cases where the volume of water is comparatively 
large and the velocity moderate. 



192. The Turbine Water- Wheel. 

water-wheel, advantage is taken of 
the reaction of the escaping jet. 
Fig. 68 represents one form of tur- 



-In the turbine 





Fig. 68,-The Turbine Water-Wheel. 

bine in perspective and in horizontal section. The wheel 
is so placed that the water may readily escape from the 
wheel after it has given motion to it. The top of the wheel 



128 NATURAL PHILOSOPHY. 

is covered, to protect it from the direct pressure of the water. 
The movable part of the wheel is seen at a, a, a, a, which is 
attached to the shaft A. The water enters below, through 
openings between fixed curved guides g, g, g, g, so inclined 
to the buckets, that on leaving the guides it strikes the 
buckets in the most advantageous direction. The wheel 
is driven partly by the momentum of the moving water, 
and partly by the weight of the water in the buckets. 
But this is not all; on running out of the buckets the 
reaction of the escaping stream also aids in turning the 
wheel. 

Turbines are constructed in a great variety of forms. Their axis of 
rotation may be either vertical or horizontal. The moving wheel may 
be either within the curved guide, in which case it is called an inside 
wheel, or it may be outside, as in Fig. 68, in which case the wheel is 
called an outside wheel. 

193. Efficiency of Water- Wheels. — By the efficiency 
of a water-wheel is meant the ratio between the energy 
delivered by the water to the wheel turned by the water 
and the energy delivered by the wheel to the line of shaft- 
ing turned by the wheel. Thus, if the power delivered by 
the water to the wheel be 60 horse-power, and the power 
delivered by the wheel to the shafting it drives be 48 horse- 
power, the efficiency of the wheel is f|- = 0.8 = 80 per cent. 



Problems. 

1. A cubical vessel is filled with water; how much greater is 
the pressure on the base of the vessel than on any of its vertical 
sides ? Arts. The pressure will be twice as great on the base as on 
any of the sides. 

2. A tank 9 feet deep is filled with water. If an opening is 
made in the side of the tank at the bottom, with what velocity 



PROBLEMS. 129 

will the water commence to escape, in feet per second and in 
centimetres per second. Ans. 24.06 feet per second. 

733.3 cms. per second. 

3. If the opening in the preceding problem has a cross-sectional 
area of 2 square centimetres and the velocity is uniform over the 
entire cross section, what will be the flow of water escaping from 
the tank in the first ten seconds, in cubic centimetres, in grammes 
and in pounds? Ans. 14,666 cubic centimetres. 

14,666 grammes. 
32.33 lbs. 

4. A city water-pipe carries water at a pressure of 70 lbs. per 
square inch above that of the atmosphere. (1) What elevation 
or head of water does this pressure correspond to in feet and in 
metres? (2) If an opening be made in the upper side of the 
pipe, how high, in feet and in metres, will the water rise in the 
issuing jet, assuming the pressure in the pipe to be sustained? 

Ans. (1 ) 161.5 feet, 49.23 metres. 

(2) 161.5 feet, 49.23 metres (nearly). 

5. A large iron tank filled with water has three openings cut 
in its side, the first four feet, the second nine feet, and the third 
sixteen feet below the surface of the water. What will be the 
velocity of flow from these three openings in feet per second and 
in metres per second ? 

Ans. (1) 16.04 feet per second, 4.89 metres per sec. 

(2) 24.06 " " " 7.334 " 

(3) 32.08 " " " 9.78 " " 

6. A turbine receives 100 horse-power from the moving water 
which drives it, and delivers 85 horse-power to the shaft which it 
drives. What is the efficiency ? Ans. 0.85, or 85 per cent. 

9 




CHAPTER X. 



PNEUMATICS. 



ol^o 



194. Properties of Gases. — Gases are bodies in which 
the average distances of the molecules are so great that 
they are practically situated beyond the limit of their 
sensible mutual attractions. In gases the repulsive tend- 
ency holds sway. Its action causes a gas to tend to ex- 
pand indefinitely, so that a small quantity of gas put 
into an empty vessel will expand until it fills the vessel 
whatever its size. 

The molecules of a gas possess great freedom of motion ; 
greater, indeed, than that possessed by liquids. The fol- 
lowing properties, characteristic of liquids, belong also to 
gases : 

(1.) Gases transmit pressure equally well in all directions. 

(2.) The downward, upward, and lateral pressures at any 
point are equal. 

(3.) Bodies weighed in air or other gas, lose a weight equal to 
the weight of the air, or other gas they displace. 

Air is taken as the type of a gas, since the general prop- 
erties it possesses belong equally to all other gases. 

195. Kinetic Theory of Gases. — According to the kinetic theory of 
matter, the molecules of a gas are in rapid motion toward and from one 
another. Since the molecules of a gas are situated beyond the limits 
of their sensible mutual attractions, these motions must take place in 

J 30 



PNEUMATICS. 



131 



straight lines, until the molecules, moving with great velocity, collide 
either against each other, or against the sides of the containing vessel. 
After each collision, the molecules are reflected and move through new 
paths in straight lines. The tension exerted by a gas contained in any 
vessel ; i. e., its tendency to expand, is caused by these collisions of its 
molecules against the sides of the vessel, or against any other surface 
immersed in the gas. Calculations show, that in the case of hydrogen 
gas at atmospheric pressures, the mean velocity of the molecules is equal 
to about 6100 feet per second (1859 metres per second). 

In the kinetic theory of matter it is common to regard the molecules 
as being separated by a repulsive force. This repulsive force exists as 
the effect of the tendency of neighboring molecules to separate after 
collision. 

196. Tension, or Internal Pressure of Gases. — 

When permitted to act, the tension of a gas causes it to 
expand or increase in volume. If not permitted to cause an 
increase in volume, the tension produces pressure against 
the walls of the containing vessel. In the case of air and 
other gases on the earth's surface, the tendency to expand is 
held in check by gravity, which may be proved as follows ; 
A bladder, Fig. 69, partly filled with air or other gas, is 
tied at the neck, and placed under a 
glass bell connected with an air-pump. 
As the air is removed from the bell, the 
gas in the bladder, being relieved of the 
pressure of the air upon it, at once ex- 
pands and fills the bladder. If, now, 
the air be again allowed to enter the 
bell, the gas in the bladder at once re- 
turns to its former volume. 




Fig, 69.— Expansion of 
Air in Vacnons Space. 



This tendency of a gas to expand on the re- 
lief of pressure, often causes a balloon to burst 
as soon as it reaches a certain elevation in the 
air. To avoid this, a valve is placed in the top of the balloon to enable 
the aeronaut to let out gas and thus relieve the internal pressure when 
necessary. 

197. The Atmosphere, the name given to the mass 
of air which surrounds the earth, consists of a mechanical 



132 NATURAL PHILOSOPHY. 

mixture of two gases, oxygen and nitrogen, in the propor- 
tion, by volume, of about one part of oxygen to four of 
nitrogen. The atmosphere contains also a small quantity 
of carbonic acid and a variable quantity of the vapor of 
water. 

The atmosphere is kept in its place by the force of 
gravity ; it is densest at the earth's surface at the level of 
the sea, and becomes rarer as we ascend, being, for exam- 
ple, rarer at the summit of a mountain. If all the air 
had equal density it would be contained in a layer or 
ocean 26,000 feet in depth ; but, owing to its diminishing 
density, the upper limit is at a far greater distance above 
the surface. 

198. Diffusion of Gases. — 

Experiment 34. — Pour equal volumes of mercury, water and oil 
into a tall jar. Observe that no matter how thoroughly they may be 
shaken together, if allowed to stand, they will soon separate into dis- 
tinct layers according to their differences of density, the mercury being 
the heaviest, falling to the bottom of the jar, the oil floating on top, and 
the water occupying an intermediate position. 

All liquids, however, will not thus separate into layers 
when mixed together ; many possess the power of dif- 
fusing, or mixing through each other, notwithstanding 
their differences of density, so that a heavier liquid will 
rise and diffuse through, or mix with, a lighter liquid 
placed on top of it. This mixing of liquids notwith- 
standing differences in density is called diffusion. 

Gases possess the power of diffusion in a marked de- 
gree. If a light gas be placed in the upper part of a 
vessel, and a heavier one in the lower part, the two will 
not remain separate, even if the vessel be kept still. The 
heavy gas will rise and the light gas will fall, until they 
have become evenly mixed or diffused. 

Diffusion of gases is a natural result of the kinetic theory of matter. 
The molecules of each gas, in their to-and-fro motions, readily move 



PNEUMATICS. 133 

into the intermolecular spaces of the other gas, and so eventually effect 
a thorough admixture. 

Every gas will diffuse into the space occupied by another gas ; i. e., 
all gases possess the power of diffusion. This is not the case with liquids ; 
some liquids will not diffuse ; as, for example, mercury and water. 

The property of diffusion is of great utility in our at- 
mosphere, in keeping the oxygen, nitrogen, and carbonic 
acid gases thoroughly mingled. Were these gases to 
settle in separate layers according to their differences 
in density, the life which now exists on the earth would 
either entirely cease, or be greatly modified. By the 
property of diffusion, we find relatively the same gen- 
eral proportion of the heavier gases in the air over the 
summits of high mountains as in the lower layers near 
the earth. 

Diffusion of gases takes place also through porous partitions. Here 
the rapidity of diffusion varies with the size of the pores and with the 
size of the molecules of the gas ; i. e., with the kind of gas. 

The gradual collapse or shrinkage of a toy gas-balloon is due to the 
loss of its contained hydrogen by diffusion into the air. 

199. Atmospheric Pressure. — Since we live at the 
bottom of an ocean of air, we must, like everything else 
at the earth's surface, sustain a pressure arising from the 
weight of the air above us. Gases, however, like liquids, 
transmit pressure equally well in all directions, and the 
equal and opposite pressures so neutralize each other that 
we do not feel the pressure which the air exerts on us. 
When, however, the pressure is removed from one side, 
the pressure on the other side is at once manifested. 

The air presses so equally on all sides of bodies, that it was long be- 
fore the existence of an atmospheric pressure was discovered. The dis- 
covery was made in 1643, by Torricelli. 

200. Torricelli's Experiment. — Torricelli's famous 
discovery was made by means of the following experi- 
ment. He took a glass tube about 33 inches long, closed 
at one end, and filled with mercury. Placing his thumb 



134 



NATURAL PHILOSOPHY. 




Fig. 70 -The Barom- 
eter, 



over the open end, as in Fig. 70, he inverted the tube and 
dipped the open end below the surface 
of mercury in a cup. When the thumb 
was taken away, the mercury did not all 
run out of the tube, a column about 30 
inches high remaining in the tube, where 
it was kept by the pressure of the air on 
the mercury in the cup. 

The atmosphere, by its weight, exerts 
a downward pressure on the surface of 
the mercury in the cup ; but the upward 
pressure against the open mouth of the 
tube is equal to the downward pressure ; 
therefore, the total pressure which holds the 
mercury in the barometer is equal to the 
weight of a column of air of the same area of cross section as 
the column of mercury in the tube, and extending upwards 
from the level of the mercury in the cup to the upper limit of the 
atmosphere. 

At the level of the sea, the pressure of the atmosphere 
will hold up a column of mercury about 30 inches (762 
mm.) in height above the level of the mercury in the cup. 
If the area of the open end of the tube be one square 
inch, this column of mercury will weigh about fifteen 
pounds. Therefore, the pressure of the atmosphere at the level 
of the sea is about equal to 15 lbs. to every square inch of sur- 
face, or about one kilogramme to the square centimetre of sur- 
face. 

201. The Barometer.— Torricelli's tube forms an in- 
strument called the barometer. 

The barometer may be regarded as a species of air-bal- 
ance. The weight on one arm of the balance is a column 
of air reaching from the level of the mercury in the cis- 
tern to the upper limits of the atmosphere ; the weight on 
the other arm is that due to the column of mercury in 



PNEUMATICS. 135 

the tube. Any variation in the pressure of the atmosphere 
causes a corresponding variation in the height of the mer- 
curial column in the barometer. 

By means of a barometer we may note the variations 
that occur in the pressure of the atmosphere. If, from 
any cause, the atmospheric pressure increases, the mercury 
rises in the barometer tube ; if the pressure decreases, the 
mercury falls. As a rule, a rise of the mercury in the 
barometer is followed by clear weather, its fall by foul 
weather. The barometer is used, both on land and sea, to 
observe approaching changes in the weather. Its use, 
however, for this purpose requires considerable experience. 

Since it is only the air above the mercury in the cup 
that keeps the mercury in the tube, it follows that if we 
carry a barometer up a high mountain, the mercury in 
the tube will fall as we ascend. The barometer, therefore, 
may be used to measure the height of mountains or other 
elevations. 

Barometers may be made with other liquids than mercury; the 
height of the column will depend on the specific gravity of the 
liquid. Thus, if water be used, the height 
will be about 34 feet ; for, since mercury 
is about 13.6 times heavier than water, 
the height would be 13.6 x 30, or 408 
inches, or about 34 feet, were it not for 
the fact that the vapor of water formed 
in the tube would somewhat decrease the 
height. 

202. The Aneroid Barometer 

is a barometer that does not con- 
tain any liquid. This barometer 
depends for its operation on the Figi 7L _ Ane ^ d Barometer , 
pressure exerted by the air against 

the surface of a short, cylindrical box, of thin elastic metal, 
partially exhausted of air. An increase in the pressure of 
the air causes the box to collapse partially ; i. e., the top 
and the bottom of the box move towards each other. On 




136 



NATURAL PHILOSOPHY. 



a decrease in pressure, the elasticity of the metal causes 
the top and bottom to move away from each other. These 
changes cause a needle to move over a graduated scale. 
The general arrangement of the parts of an aneroid ba- 
rometer is shown in Fig. 71. 

203. Pressures Expressed in Atmospheres. — It is 
convenient to express the pressure exerted by a column 
of liquid or gas, in units of pressure called atmospheres. 
Thus, a pressure equal to 15 lbs. per square inch is called 
a pressure of one atmosphere ; a pressure of 60 lbs. to the 
square inch is called a pressure of four atmospheres, and 
so on. 

204. The Air- Pump. — In order to manifest the pressure 
which the atmosphere exerts on any object , it is necessary 

to remove the pressure of 
the air from one side of 
the object. This is most 
conveniently done by 
means of an apparatus 
called an air-pump. 

Fig. 72, represents a 
form of air-pump. An 
air-tight piston P, moves 
in the cylinder 0. Open- 
ings are provided at a and 
c, in the bottom and top 
of the cylinder, and at ft, 
in the piston. These openings are alternately shut and 
opened by contrivances called valves. In the air-pump 
these valves all open upwards. The cylinder is con- 
nected by a tube e, with a flat plate M, on which is 
placed a glass vessel R, called the receiver, the base of 
which is carefully ground so as to ensure an air-tight 
joint. By successive movements of the piston, the air 
in the receiver i?, is gradually removed, when the receiver 
is said to be exhausted. 




Fig. 72— Air-Pnmp. 



PNEUMATICS. 137 

The operation is as follows : When the piston rises, say from the bot- 
tom of the cylinder, a vacuum is left below it, into which some of the 
air from the receiver R, at once passes, lifting by its tension the valve a. 
When the piston descends, the air in (7, is compressed, the valve a, shut, 
and the valve 6, opened, and the air below the piston is transferred 
above it. As the piston again rises, more air pssses from B, to the cyl- 
inder, while the air above the piston is forced out of the cylinder through 
the valve c. 

Valves in an apparatus are designed for the passage of liquids or gases 
through the apparatus. It is easy to remember how the valves open 
and shut. For example, in the air-pump, the air contained in any ves- 
sel is removed, or the vessel exhausted, by transferring the air from 
such vessel through the body of the pump to the outer air. The three 
valves of an air-pump must, therefore, open upwards, because the air 
passes through the pump-barrel in this direction. 

205. Illustrations of Atmospheric Pressure. — The 

glass receiver R, may easily be lifted from the plate of the 
air-pump, when not exhausted. But when the receiver is 
exhausted, the pressure of air on the outside holds it so 
firmly to the plate, that, if the receiver is moderately large, 
it will be almost impossible for an ordinarily strong person 
to remove it from the plate, until the air is again allowed 
to enter. 

Two hollow hemispheres of brass, provided with smooth 
plane edges, if simply pressed together, so as to form a 
hollow sphere, and then connected with an air-pump so 
that the air may be removed from the inside, are held to- 
gether so firmly, by the pressure of the air on the outside, 
that it is difficult to pull them apart. 

When a receiver with an open top, over which a piece 
of bladder has been tightly stretched, is placed on the 
plate of an air-pump and exhausted, the pressure of the 
air on the bladder bursts it with a loud report. 

206. Simple Experiments in Atmospheric Pres- 
sure. — The following experiments in atmospheric pres- 
sure can be shown without the use of an air-pump. 

Experiment 35.— Place the open end of a hollow key to the mouth, 



138 



NATURAL PHILOSOPHY. 



and, after vigorously sucking out the air, quickly press the end against 
the lip. Observe that the key will be held there by the pressure of the 



Experiment 36.— Select a small wineglass with a smooth edge. 
Place some small pieces of tissue-paper loosely under the glass, and set 
fire to them. As soon as they are nearly consumed, quickly press the 
glass against the hand. Observe that it will then be held against the 
hand with considerable force. The heat expands the air and drives part 
of it out of the glass, which, on cooling, is then held against the hand by 
the outside atmospheric pressure. 

Experiment 37. — Fill a smooth-edged tumbler with water; place a 
piece of stout paper over the top, and, holding the palm of the hand 
against the paper, slowly invert the tumbler. Though the hand be now 
removed from the paper, the water will not run 
out, because the pressure of the air holds the 
paper firmly against the tumbler as shown in 
Fig. 73. 

Experiment 38.— Select an empty tomato 
can, from the top of which the small round piece 
of tin has been removed, leaving an opening 
about two inches in diameter. Tie a piece of 
mosquito-netting firmly around this end of the 
can, stretching it smoothly over the top with the 
fingers. Fill the can with water and place a 
piece of smooth, stiff paper over the open end, 
and invert as in the previous experiment. Observe that the paper will 




Fig. 73.— An Experiment 
in Atmospheric Pressure. 





Fig. 74.— An Experiment in . 
Pressure. 



Fig. 75.— An Experiment 
in Atmospheric Pressure. 



then be held against the can by the pressure of the air. Now holding 
the can as shown in Fig. 74, cautiously slide the paper from the netting, 



PNEUMATICS. 139 

and the water will still remain in the can, although the open end is only pro- 
tected by the mosquito-netting. 

Experiment 39. — Prepare a can as described in Experiment 38, 
and punch a hole with a nail in the bottom of the can. Holding a 
finger firmly over the hole, fill, invert, and remove the paper as before, 
and the water will not run out; now remove the finger momentarily 
from the hole, as shown in Fig. 75, and observe that, the pressure of the 
air being then exerted downwards on the water, as well as upwards, the 
water flows out by its own weight. Eeplace the finger, and the flow 
ceases, since the pressure of the atmosphere is greater than the weight 
of the water. This curious experiment proves, 1, Atmospheric pres- 
sure ; 2, Adhesion of water to the netting, and, 3, Cohesion of the mole- 
cules of the water. 

The common leather sucker depends for its operation on 
the pressure of the air. 

207. Buoyancy of Air. — The Law of Archimedes. 

— A body weighed in air loses a weight equal to the 
weight of the air it displaces. For ordinary purposes this 
loss of weight may be disregarded ; but it becomes more 
appreciable as the bulk of the thing weighed exceeds the 
bulk of the weights used to balance it. 

Suppose, for example, that a pound of feathers be bal- 
anced in air by a pound of lead; then, since the bulk of 
the feathers is greater than that of the lead, the buoyancy 
of the air must decrease the weight of the feathers more than 
it does the weight of the lead, and, therefore, more than one 
pound of feathers is required to balance one pound of lead in air. 

208. Balloons. — A solid lighter than water, when com- 
pletely immersed in water, unless held in place, will rise 
until it floats, with a certain portion only of its mass below 
the water. It rises, because when completely immersed it 
is thrust upwards by the force of buoyancy, which is then 
greater than its weight. 

Balloons rise through air for the same reason ; for, be- 
ing filled with some light gas or heated air, their weight, 
which tends to pull them down, is less than the buoyant 
force of the displaced air which tends to push them up- 
wards. When these two forces are exactly equal, the bal- 



140 NATURAL PHILOSOPHY. 






loon will neither rise nor fall. The ascensional or lifting 
power of a balloon can, therefore, be found by subtracting 
the weight of the balloon, enclosed gas and car, from the 
weight of an equal bulk of air. 

At the sea level, and at ordinary temperature and pressure, 100 cubic 
inches of air weigh about 31 grains; or, 1 cubic centimetre of air at the freez- 
ing point of water and 1 kilogramme per sq. cm. weighs 0.001252 gramme. 

209. Boyle's or Mariotte's Law. Effect of Pres- 
sure on the Volume occupied by a Gas. — Gases, as 

we have seen, are the most compressible forms of mat- 
ter. As the pressure on any bulk of gas is increased, its 
volume is diminished ; conversely, as the pressure is de- 
creased, the tension of the gas causes its volume to in- 
crease. The law according to which these changes occur 
was discovered independently by Boyle and by Mariotte, 
and may be expressed as follows : 

At the same temperature, the volume occupied by a given bulk 
of gas is inversely proportional to the pressure it supports. 

This law is nearly true for all gases. 

Suppose, for example, that a certain quantity of air, 
at the ordinary pressure of the atmosphere, occupies the 
volume of one quart ; then, if the pressure on this quan- 
tity of air be increased to two atmospheres, its volume 
will be reduced to one-half of a quart ; if the pressure be 
increased to three atmospheres, its volume will be reduced 
to one-third of a quart ; if to ten, or one hundred atmos- 
pheres, to y 1 ^ or y^o of a quart. Again, if the pressure 
of one atmosphere on the quart be reduced to one-half 
an atmosphere, the tension of the air will cause it to ex- 
pand to two quarts ; if it be reduced to y^- of an atmos- 
phere, it will expand to one hundred quarts. The ability 
of a gas to expand on the relief of pressure appears to be un- 
limited. 

210. Experimental Verification of Boyle's Law. — 
A glass tube h, bent as shown in Fig. 76, is closed at V, 
and open at h ; mercury is poured into the tube at h, until 



PNEUMATICS. 



141 



the level is the same in both tubes, as, for example, at I a. 
The air in the closed space above £, is then at the pressure 
of one atmosphere. If, now, mer- 
cury be poured in the open end at 
hj until the air in the space above 
/, is reduced one-half in bulk, say 
until the level in the long arm is 
at a', then the length h a', will be 
found to be the barometric height, 
or sensibly 30 inches. An addi- 
tional pressure of one atmosphere 
due to the 30 inches of mercury 
has, therefore, been added to the 
pressure of the air, making two at- 
mospheres, and these tw r o atmos- 
pheres of pressure have reduced 
the volume of the air to one-half 
its volume at one atmosphere. 

211. Effect of Pressure on 
Specific Gravity or Density. — 

Since the mass of a gas remains 
the same, however its volume may 
be changed by pressure, the density 
or specific gravity must increase, or 
the density must be proportional to the 
pressure. 

Thus if, under a pressure of one 
atmosphere, the density of a gas 
be 1, then, under a pressure of two atmospheres, since its 
volume becomes |-, its density becomes 2, and so on. 

Since the lower layers of the atmosphere sustain the 
weight of the upper layers, the density of the air near 
the sea-level is greater than that at the top of a moun- 
tain. 




Fig. 76.— Experimental Veri- 
fication of Boyle's Law. 



212. Apparatus Depending for its Action on At- 



142 



NA TUBAL PHILOSOPHY. 



mospheric Pressure. — In the following apparatus ad- 
vantage is taken of the pressure of the atmosphere : 

1. The Siphon. — The siphon consists of a tube bent as 
shown in Pig. 77. When the shorter arm is placed below 
a water-surface, and the tube exhausted of air by the suc- 
tion of the mouth applied at 6, the pressure of the air on 





Fig. 77 -The Siphon. 



Fig. 78— The Snction-Pump. 



the water in m, causes the water to rise through the height 
m n, and to flow out of the open end b. The greater the 
difference of level a 6, between the water surface m, and 
the open end 6, the greater the velocity with which the 
water escapes. 

2. The Suction-Pump for Raising Water. — In the common 
suction-pump, Fig. 78, water is raised from a well into the 
body of the pump by the pressure of the atmosphere. In 
its simplest form, this pump is essentially the same as the 
common air-pump. The valves open upwards; one or 
more of these valves b 6, are placed in the piston, and one 
a, at the lower end of the cylinder, or pump-barrel. As 
the piston is raised, a vacuum is left below it in the pump- 
barrel, into which the air rushes from the pipe dipping 
down into the well W. As the air is thus sucked out of 
the pipe, the pressure of the air on the water in W y forces 



PROBLEMS. 



143 



it up through the valve a. As the piston descends, the 
valve a, closes, the valves b 6, open, and the water passes 
above the piston. When the piston is again raised the 
water escapes at the mouth of the pump at D. In the 
figure, the valves are represented in the position they 
would occupy in the up-stroke of the piston. 

3. The Force-Pump. — In the force-pump, Fig. 79, there 
is no valve in the piston P. A pipe T 7 , en- 
ters the side of the cylinder near the bot- 
tom. A valve a, which opens outwards, 
is placed where this tube enters the cylin- 
der. There is, as in the suction-pump, a 
valve 6, at the lower end of the pump- 
barrel. On the downward stroke of the 
piston, the water, instead of passing above 
the piston, is forced through the valve a, 
up through the pipe T. In the figure the 
valves are represented in the positions 
they would occupy during the up-stroke 
of the piston. 

The height mn, through which the wa- 
ter is raised by the pressure of the air in the siphon, the 
suction-pump, or the force-pump, can never exceed about 
34 feet, since, as we have seen, a column of water of this 
height exerts a pressure equal to that of the atmosphere. 
In practice, pumps seldom raise water higher than 28 feet 
from the level of the well to that of the lower valve. 




Fig, 79— The Force- 
Pump. 



Problems. 

1. If the back of the hand has an area of about 28 sq. in., what 
force in pounds weight and in kilogrammes weight would be 
necessary to lift the hand against the pressure of the atmosphere, 
assuming the latter to be 15 lbs. per sq. in., if the pressure were 
entirely removed from the lower surface of the hand ? 

420 lbs. 

190.5 kilos. 



144 NATURAL PHILOSOPHY. 

2. If a barometer tube is filled with glycerine the specific grav- 
ity of which is 1.27, what will be the height of its column in 
inches and in centimetres, when the mercurial barometer stands 
at thirty inches? Arts. 321.1 inches. 

815.7 cms. 

3. What would be the height of the column in the preceding 
barometer tube if the glycerine were replaced by pure water? 
Express the result both in inches and in centimetres? 

Arts. 407.8 inches. 
1036 cms. 

4. If the entire surface of the human body is 20 square feet, 
what is the total pressure supported by it, taking the pressure of 
the atmosphere as 15 lbs. per square inch ? Express the result in 
pounds weight and kilogrammes weight. 

Arts. 43,200 lbs. weight. 
19,595 kilos, weight. 

5. A room 15 feet long, 12 feet wide, and 10 feet high, is filled 
with dry air at 0° C. at a pressure of one kilogramme per sq. cm. 
What is the total weight of the air in the room in grammes, in 
kilogrammes and in pounds? Am. 63,819 grammes. 

63.819 kilogrammes. 
140.7 lbs. 

6. What is the total pressure of the air upon the floor of the 
above room in pounds and in kilogrammes, taking the pressure as 
15 lbs. per sq. in.? Arts. 388,800 lbs. 

176,365 kilos. 




PART III. 
Sound and Light. 

CHAPTER XI. 

NATURE OF WAVE MOTION. 

213. The Nature of Vibrations.— 

Experiment 40. — Attach a string to a plumb-bob, or other suitable 
weight, and, holding the free end of the string in the hand, allow the 
weight to swing to-and-fro like a pendulum. Observe that the time 
required for the pendulum to complete a to-and-fro motion is prac- 
tically the same, whether it swings through a great or through a small 
distance. 

Experiment 41. — Set the pendulum of the preceding experiment 

into vibration, by moving its bob. Note the time that it continues 

I swinging to-and-fro when released, before it comes to rest. Eaise the 

i bob higher than before, start the pendulum a second time, and observe 

that it will continue swinging for a longer time before coming to rest. 

A tightly stretched wire or string, such as a piano wire 
or a violin string, when momentarily moved out of its 
position of rest, will vibrate or move to-and-fro, like a 
pendulum. The sides of a bell, when struck, will also 
vibrate or move to-and-fro like a pendulum, or like the 
piano or violin string. 

These to-and-fro motions, whether of the pendulum, of 

10 N 145 



146 



NATURAL PHILOSOPHY. 



the wire, of the string, or of the sides of the bell, are called 
vibrations. 



214. The Cause of the Vibrations of a Pendulum. — 

Vibrations or oscillations are never set up in a body with- 
out the expenditure of energy on the body. A body 
when vibrating, therefore, possesses more energy than it 
does when at rest. 

In order to set a pendulum in motion, work must be 
done on the pendulum against the force of gravity ; i. e., 
the bob of the pendulum must be raised, say to the posi- 
tion c, Fig. 80, through the vertical distance c e. If the 

pendulum bob weighs one 
pound, and the distance c e, 
is one foot, then, disregard- 
ing the weight of the rod and 
friction, the amount of work 
done on the pendulum bob 
will be one foot-pound. 




As the pendulum swings to-and- 
fro, it expends its energy, or does 
work, in overcoming the resistance 
of the air, and in friction against its 
point of support. If no additional 

energy be given to the pendulum, it will come to rest as soon as the 

amount of this work is equal to one foot-pound. 



/ b f e 

Fig. 80.— Kinetic and Potential En- 
ergy in Moving Pendulum. 



As the vibrating pendulum gradually expends its energy, 
the amplitude of its vibrations, i. e. the distance through 
which the pendulum swings, becomes less ; but the period 
of the vibration, or the time required to complete one to- 
and-fro motion from d to c, and from c back to d, remains 
the same for all amplitudes, provided these are small. 

215. Kinetic and Potential Energy in a Pendulum. — If the pen- 
dulum encountered no resistance to its motion, either from the air or 
from friction, it would move to-and-fro forever. The energy imparted 



NATURE OF WAVE MOTION. 147 

to the pendulum to set it in motion, becomes alternately potential and 
kinetic. When the pendulum reaches the position a c, all its energy 
becomes potential. When the position a 6, is reached on the downward 
swing, all the energy is kinetic ; at a d, all the energy is again poten- 
tial. As the pendulum swings to-and-fro, all its energy is potential at 
the highest points of its motion, and all kinetic at the lowest points. At 
any intermediate point, as at g, the pendulum possesses an amount of 
kinetic energy represented by the distance h g, through which it has 
fallen, and an amount of potential energy represented by the distance 
g /, through which it still has to fall. In any position, the sum of the 
kinetic and potential energies is a constant quantity. 

216. Elasticity Necessary to Vibrations.— Vibra- 
tions cannot be produced in inelastic substances, such 
as dough or putty. A rod of lead will not vibrate like 
the rod of steel shown in Fig. 81, because lead has but 
little elasticity. 

In the case of the pendulum, the work done on the pendulum against 
the force of gravity, permits energy to become stored as potential energy. 
In the case of a vibrating steel rod, the work done on the rod against the 
forces of molecular attraction and repulsion, developed through its elas- 
ticity, permits the energy to become potential. In an inelastic bar these 
forces cannot be called into play, since no means exist for the energy 
acting on the bar to become alternately potential and kinetic, and vibra- 
tions are, therefore, impossible. 

217. Energy Expended by Vibrating Bodies. — As a 

vibrating body moves to-and-fro, it expends its energy, or 
does work, in setting up a wave motion in the air or other 
medium which surrounds it. 

Energy is always required to cause a body to vibrate, 
and the body will cease vibrating as soon as it has ex- 
pended all the energy it has received. 

218. All Energy of Vibrations Alternately Kinetic 
and Potential. — The energy possessed by any vibrat- 
ing body is alternately kinetic and potential. The vi- 



148 NATURAL PHILOSOPHY. 

brating rod ad, Fig. 81, has all its energy potential when 
in the position db, or d c, at the farthest points 
of its swings. On its return to d a, from either 
of these positions, all its energy is kinetic. 
When the rod is at d 6, or d c, work has been 
done in producing flexure or bending, all the 
kinetic energy being converted into potential 
energy, represented by the elasticity of flexure. 
The molecules of the rod are disturbed from 
their positions of equilibrium by being pulled 
farther apart on the convex side of the bar 
and crowded together on the concave side. 
The forces of molecular attraction and repul- 
sion, thus brought into action through elas- 
ticity, produce respectively a push and a pull, 

brating Rods, that carry the bar to the position a d, where, 
the molecules being in their normal positions, 

all the energy becomes kinetic. This energy of motion 

then carries the bar to c d, where all the energy is again 

potential. 

219. The Vibrations of a Cord Fixed at One End.— 

Experiment 42.— Fasten a cord A B, at A, as shown in Fig. 82, and 
smartly shake it by the hand at B. Observe that a wave, as indicated by 



d 




d b 

Fig. 82.— Waves in a String, 

the curved line BaEbDcdA, will move along the cord from B to A, and 
that on reaching A, the wave will be reflected, and will move again to- 
ward the hand along the lower curved line, and that these motions will 
give the particles of the string the appearance of moving alternately from 
B to A, and from A to B. 

In vibrations of this character the pulses and not the 
particles of the string, move along the string from one 
point to another; the particles of the string merely rise 



NATURE OF WAVE MOTION. 



149 



and fall, being sometimes above the straight dotted line, 
as at B a E, and sometimes below it, as at E b D. 

220. No Continued Onward Motion of the Medium 
in Waves. — Wave motion is seen in the waves produced 
in a carpet that is being shaken, or in a field of grain, 
over which the wind is blowing. Here, although the waves 
move forward, there is evidently no continued onward 
motion either of the carpet or of the grain. 

There is no onward motion of the water, when waves 
are started in deep w T ater. Light bodies, floating on the 
surface, merely rise and fall with the waves, but do not 
continue to move onward with them. 

In wave motion the particles move alternately backwards and 
forwards through comparatively small distances, while the waves, 
unless turned out of their course, move through considerable 
distances in one direction only. 

Thus, let the dots between D and B, Fig. 83, represent a 



I)\ 



1 


^tffffff 


1 


Ifcl. . ' 










d M 

"■•• •** •Jv v 


]rruj5W" 



nB 



Fig. 83 —Motion of the Particles, 

row of particles in a string which, when at rest, will have 
the positions shown in the straight line D B. If a wave 
moves along the string from D to B, the particles do not 
move from D towards B ; they simply move above or be- 
low the straight line D B, as shown by the arrows. 

As in the case of the pendulum, the vibrations set up in cords, in rods, 
or in elastic media generally, perform their to-and-fro motions in equal 
times, whatever the distance may be through which these motions take 
place ; i. e. whatever their amplitude. It is for this reason that a piano 
string continues to emit the same note throughout its vibrations, even 
when the string has almost come to rest. 



150 NA TUBAL PHILOSOPHY. 

221. Velocity of Waves. — The velocity of a wave is 
the distance through which the wave moves in a given 
time. 

If the time be noted that a wave takes to move from 
one end to the other of a long wire or rope, it will be 
found that in the same wire or rope, whether the waves 
be long or short, the separate pulses move from one end 
to the other in the same time, but that in wires or ropes 
of different materials, the waves travel with different 
velocities. The waves which produce sound travel in the 
air with the same velocity, whether they are the short waves 
which produce the shrill tones, or the long waves which 
produce the grave tones. 

222. The Frequency, or the Number of Vibrations 
per Second. — The number of complete vibrations, or to- 
and-fro motions, which a vibrating body makes in one 
second, is called the frequency of its vibration. 

223. Direction of the Vibration. — During vibration 
the particles of the vibrating body may move in one of 
three different directions : 

(1.) At right angles to the length of the body ; i. e. directly 
across the length, as in a tightly stretched cord or wire ; 
such vibrations are called transverse vibration?. 

(2.) In the direction of the length ; as in the case of a 
return ball, where a rubber cord is alternately lengthened 
and shortened by the to-and-fro motions of a ball attached 
to one end of the cord. Such vibrations are called longi- 
tudinal vibrations. 

(3.) In a direction spiral or curved to the length ; as 
when a string with a ball attached to one end is twisted, 
and then allowed to untwist, and twist again. Such vibra- 
tions are called torsional vibrations. 

224. Vibrations of a Stretched Cord.— An elastic 
cord or wire a 6, Fig. 84, tightly stretched between the 



NATURE OF WAVE MOTION. 



151 




Fig. 84,— Vibration of a Stretched Cord. 



points a and 6, if raised to the position a c 6, and then 
released, will move to- 
and-fro on opposite sides 
of its position of rest 
a e b. Each complete 
motion from c to d, 
and back from d to 
c, is called a vibration. 
That is to say, as in 
the case of the pendulum, each complete vibration con- 
sists of a to-and-fro motion. 

225. Laws for the Transverse Vibrations of Cords. 

— If we halve the length of a cord we double the number 
of its vibrations per second. If we double the length of 
a cord we halve the number of its vibrations per second. 
If we increase the stretching weight four times, we double 
the number of its vibrations per second. If we double 
the diameter of a cord we halve the number of its vibra- 
tions. 

In a piano, the short, thin wires vibrate rapidly and give 
the high shrill tones, w T hile the long, thick wires, vibrating 
more slowly, give the low grave tones. 




CHAPTER XII. 



THE TRANSMISSION, 
TION 



REFLECTION 
OF SOUND. 



AND REFRAC- 



-«k£©<o 



226. The Cause of Sound.— 

Experiment 43.— Sound a bell by striking it. Observe that when 
sounding loudly, a rapid shaking of its sides may be seen, and that when 
sounding less loudly, these movements may be detected by touching the 
sides lightly by the hand. Observe also, that when these shakings cease, 
the sound ceases, as may be proved by pressing the hand against the sides, 
thus completely stopping the vibrations, when the sound at once ceases. 

In the above experiment the bell sounds only while it 
continues vibrating. It can be shown that all bodies are 
vibrating while producing sound. 

Sound is caused by the shakings or vibrations of a sounding 
or sonorous body. 

A tuning-fork consists of a bar of steel, shaped as shown 
at a 6, Fig. 85, and firmly supported on a hollow case 
e, of dry wood. When the fork is 
sounded by rubbing with a rosined 
bow, the arms a 6, move alternately 
towards and from each other, setting 
the air around them into waves, and 
producing a musical sound. 

Experiment 44.— Partially fill a thin glass 

goblet with water, and rub the moistened fingers 

lightly against the edge, so as to produce a clear musical note. Observe 

that the surface of the water is ruffled with miniature waves, produced 

152 




Fig. 85— Tuning-Fork. 



TRANSMISSION OF SOUND. 153 

by the vibration of the sides of the goblet. The waves may be produced 
more readily, by drawing a rosined bow over the edge of the glass. 

227. Double Meaning of the Word Sound. — The 

word sound has a double significance : 

(1.) The sensation produced when the effects of sound- 
waves reaching the ear are transmitted to the brain. 

(2.) The waves in the air or other medium which cause 
the sensation. 

The assertion that there would be no sound if there were no ears, is 
true, if by the word sound is meant the sensation ; since, if there were 
no organs of hearing, there could be no transmission of the effect of the 
sound-waves to the brain and, therefore, no sensation. If, however, the 
word sound be used to signify the thing causing the sensation ; viz., the 
waves in the air, which probably is the sense in which the word is most 
frequently employed, then the assertion is untrue, since the existence 
of the sound-waves does not depend on the existence of an ear or brain. 

A similar double significance is given to the words light, taste, and 
smell. The sun would shine, and a dish of strawberries would possess 
both fragrance and taste, whether there were an eye to see, a tongue 
to taste, or a nasal organ with which to smell. 

228. Manner in which the Vibrations are Con- 
veyed from the Vibrating Body to the Ear. — As a 
vibrating body moves to-and-fro, it sets the air surround- 
ing it into waves. These waves move out from the body 
in all directions, and reaching the ear, produce the sensa- 
tion of sound. 

229. Nature of Sound- Waves. — While the vibrating 
body, such as a bell, is sounding, its sides, in moving out- 
wards, crowd the particles of the air immediately in front 
of them into a smaller space, thus condensing the air. 
When its sides are moving in the opposite direction, the 
particles of air expand, in order to fill the space left 
empty by the moving sides, thus effecting an expansion 
or rarefaction of the air. A complete vibration of the bell 
consists of a single motion of its walls inwards and out- 
wards. A complete wave motion of the air consists of a 



154 NATURAL PHILOSOPHY. 

single consecutive condensation and rarefaction of the 
air. The sound-waves surrounding the sonorous body 
in the shape of spherical waves, called waves of condensation 
and rarefaction, consist of alternate condensations and rare- 
factions of the air. 

The motion of the air particles in a sound-wave is alter- 
nately backwards and forwards in the same direction as that 
in which the wave is advancing ; that is to say, sound-waves 
are longitudinal vibrations. The greater the amount of 
energy in the vibrations of a sonorous body, the greater 
will be the number of particles of air crowded into the 
condensed place, and the smaller the number of particles 
of air left in the rarefied space, the louder will be the 
sound produced. 

Some idea of the nature of sound-waves may be obtained from an in- 
spection of Fig. 86, where the shaking of the bell is represented as 





Figi 86,— The Transmission of Sound. 



causing waves or condensations and rarefactions in the air around it. 
In these waves, the particles of air are alternately crowded together and 
separated from one another, as shown by the dark and light shadings, 
and move in straight lines, alternately directly from and towards the 
bell. 

The nature of the motion of the particles of air may be 

roughly represented by the following experiment. 

Experiment 45. — Place a number of glass marbles in a straight 
wooden trough, so that they touch one another. Cause a marble at one 



TRANSMISSION OF SOUND. 155 

end of the trough to roll against the marble next to it. Observe that the 
marbles will not move on together, but that the first gives its motion to 
the second, and then stops; the second gives its motion to the third, and 
so on, through all, to the end marble, which, having no marble to which 
to give its motion, moves on. A similar action takes place in the case 
of sound-waves : the vibrating body strikes the particles of air near it ; 
these give their motion to the particles of air beyond them, and then 
stop ; and these particles to others beyond them, and so on until at last 
the waves reach the ear, and we hear the sound. 

The more rapid the vibrations of the sonorous body, 
i. e. the greater the number of vibrations per second, the 
shriller will be the sound produced. 

The greater the energy imparted to the sonorous body 
producing the sound, or the greater the amplitude of the 
sound-waves, the louder will be the sound produced. 

The air particles do not continue to move onward from the vibrating 
body until they reach the listener' s ear. They move a short distance, 
condensing the air before them, and then stop and move in the opposite 
direction. Meanwhile, the air condensed by the first pulse expands or 
moves outwards and condenses the air in front of it, and then moves 
backwards. This condensed air then expands and condenses the air in 
front of it, until finally, the last condensed or rarefied pulse enters the 
listener's ear. 

230. A Medium Necessary to Transmit Sound. — 

Since sound is transmitted by waves, some elastic medium 

to be set into waves must exist between 

the sounding body and the listener's ear, 

in order that the sound may be carried 

from one point to another. If a bell be 

struck in a vacuum, no sound will be 

heard, since there is no medium to be 

set into waves to carry the sound. In 

Fig. 87, a bell is suspended by a thread Fig, 87 -Bell in 

inside a glass globe B. If the air be ® lole ' 

removed from the globe by means of an air-pump, no 

sound will be heard when the bell is struck. 

Sound-waves are transmitted through air because the 
air is elastic. As we have already seen, any elastic sub- 




156 



NATURAL PHILOSOPHY. 



stance -will transmit sound. Therefore, gases, liquids, and 
solids may all transmit sound. 

Experiment 46. — Eing a bell under water. Observe that the sound 
may be heard by those standing near the water. Here the water must 
have transmitted the motions of the bell. The sound of the bell will be 
more distinctly heard if the hearer's ear is under the water. 




Fig. 88.— The String-Telephone. 

Experiment 47. — Eemove the bottoms from two small tomato cans ; 
moisten a piece of bladder or stiff paper, stretch it tightly over the open 
end of each, and secure by tying. When quite dry, pierce a hole in the 
middle of the bladder or paper, with a large darning needle. Get a piece 
of string 15 or 20 feet long, and run one end through each of these holes 
from the outside of the can to the inside. Tie a piece of match-stem to 
each end of the string, or knot the string to prevent its slipping out. 
Observe, that if now the string be stretched rather tightly, a person by 
placing an ear at the opening of one of the cans, as shown in Fig. 88, 
may distinctly hear whatever another person whispers into the open end 
of the other can. This instrument is called the string-telephone. 

Experiment 48. — Try the same experiment, using cigar boxes and 
wire instead of the tomato can, string and bladder. Bore a hole in the 
bottom of each box for the insertion of the wire. Talk into, or listen at, 
the open end of the boxes. The wire may then be stretched for a con- 
siderable distance in a straight line, as across the street from one house to 
another. 

231. Velocity of Sound in Air. — Time is required for 
sound to travel from one place to another. We can see a 



TRANSMISSION OF SOUND. 157 

distant man strike a blow with a hammer before we hear 
the sound. During a thunder storm we see the light- 
ning before we hear the thunder. 

By measuring the distance through which sound-waves 
move in a given time, the velocity may be determined by 
dividing the distance by the time ; or, 

V = ^ 

y T 

As a result of many careful measurements, the velocity 
of sound in air, at the temperature of melting ice, or 32° 
F., is 1090 feet, (332.2 metres) per second. 

The velocity of sound in all elastic media diminishes with the den- 
sity of the media. Therefore, so far as density is concerned, sound 
would move less rapidly through liquids and solids than through gases. 
The velocity, however, increases with the elasticity of the media, and 
since the increase of elasticity in liquids and in solids is greater than the 
increase in density, the velocity of transmission is greater in liquids and 
in solids than in gases. 

The velocity of sound in water is about four and one- 
half times greater than its velocity in air. 

232. Effect of Temperature on the Velocity of 
Sound. — The velocity of sound in air increases with the 
temperature. This is due to the fact that an increase of 
temperature both decreases the density, and increases the 
elasticity. 

In air the velocity of sound increases about 1.1 feet per 
second, for each degree of the Fahrenheit thermometric 
scale. 

When allowance is made for the difference in temperature, the ve- 
locity of sound is the same in the upper and less dense regions of the 
atmosphere as at the surface of the ground, because although the den- 
sity is less in the upper regions, the elasticity is also less to the same 
degree, and the ratio of elasticity to density, upon which the velocity 
depends, remains unchanged. 

233. Velocity of All Ordinary Sounds the Same. — 



158 NATURAL PHILOSOPHY. 

We have seen that in the same medium all sound-waves 
travel with the same velocity, no matter whether the waves 
be long or short. All sounds, therefore, whether shrill or 
grave, loud or feeble, must travel with the same velocity. 
Were this not the case, it would be impossible to obtain 
pleasing effects from the music of an orchestra, when at 
any considerable distance from it. 

Sound travels faster with the wind than against it, the 
sound-waves being carried bodily forwards when travelling 
with the wind, and backwards when travelling against it. 

234. Acoustic Shadow. — When an intervening object, 
such as a house or high wall, prevents the free onward 
movement of sound-waves, an acoustic shadow is pro- 
duced, the shape of which, like that of shadows cast by 
light, depends on the shape of the intervening object. 

To a distant observer, the roar of a locomotive at once 
ceases on entering a tunnel. 

Acoustic shadows are less distinctly marked than are those cast by 
light, because the sound-waves are so much longer than the waves which 
produce light. 

235. Reflection of Sound. — When nothing interferes 
with their progress, sound-waves move in all directions in 
straight lines. But when they meet a suitable obstacle, 
sound-waves, like elastic bodies, are reflected or thrown 
off at an angle equal to that at which they struck the 
obstacle. This change in the direction of sound-waves is 
known as the reflection of sound. 

The smooth and hard surfaces of elastic bodies are the 
best reflectors of sound-waves. A smooth water surface 
forms an excellent reflector of sound. Cloths, curtains and 
other draperies, scarcely reflect the waves at all. 

236. Echoes. — An echo is a sound heard by means of 
sound waves reflected by a distant body. 

In order to produce an echo it is necessary : 

(1.) That there should be a fairly extended surface 



TRANSMISSION OF SOUND. 159 

capable of reflecting sound-waves and thus throwing them 
back again to the hearer's ears. 

(2.) That the distance of this reflecting surface be such 
that the direct sound ceases before the reflected sound is 
heard. 

In ordinary speech there are about five syllables uttered 
in each second. If, therefore, the reflecting surface is at 
such a distance from the speaker, that it takes one-fifth of 
a second for the sound-waves to move from him to the re- 
flecting surface and back again to his ear, then, after he 
has ceased speaking, and all sounds of his voice have 
died away, he will hear the last syllable he uttered. The 
first syllable uttered is reflected to him and reaches his 
ear just as he begins the second syllable, but he does not 
hear it as a distinct sound. 

At the temperature of 60° F. (15.5° C), the velocity of sound is 
about 1120 feet (341.3 metres) per second. During the one-fifth of a 
second, the waves would travel 224 feet. If, therefore, the speaker is 
standing in front of a reflecting surface which is 112 feet distant, and is 
speaking at the rate of five syllables per second, the last syllable will 
be heard after all the direct sound has ceased. If the reflecting sur- 
face is 224 feet distant, the last two syllables will thus be heard ; if it 
is 560 feet, the last five syllables will be heard after the speaker ceases 
talking. 

Very sharp, quick sounds produce a less permanent effect on the ear, 
and may, therefore, cause distinct echoes when the reflecting surface is 
less distant. 

If the time required for the sound-waves to move toward 
or from the reflecting surface is less than one-fifth of a 
second, the reflected sound is not heard as a separate 
sound, but is blended with the direct sound. 

If the reflecting surface is so near the speaker that the 
direct and reflected sounds reach the ear at nearly the 
same time, the original sound is prolonged and strength- 
ened, otherwise the two sounds produce confusion. 

In a properly proportioned hall, the voice of a speaker 
is strengthened by the waves, reflected from the walls and 



160 



NATURAL PHILOSOPHY. 



ceiling, reaching the ear at nearly the same time as the 
direct sound. When, however, the hall is large, the re- 
flected sound is apt to confuse the direct sound by the 
partial echoes produced. The confusing effects caused 
in this way in large empty halls, are greatly diminished 
when the halls are crowded, since the bodies of people 
are bad reflectors. Curtains and drapery have a similar 
effect. 

When the source of sound is between two opposite walls, 
or walls very nearly opposite, the waves are thrown alter- 
nately back and forth between the walls, thus repeating 
the original sound many times. These echoes are called 
multiple echoes. 

237. Whispering Galleries. — If two curved mirrors, 
A and B, be placed facing each other, as shown in Fig. 
89, and any sounding body, as a watch, be suspended 




Fig. 89 —Reflection of Sonnd- Waves, 

at a certain distance in front of the mirror A, the waves 
after reflection from both mirrors, will collect at a point 
0, in front of the mirror B. From whatever part of 
the mirrors the waves have been reflected, they will all 
reach the point (7, at the same time. The ticking of the 



TRANSMISSION OF SOUND. 161 

watch may, therefore, be distinctly heard by a person list- 
ening as shown in the figure. 

Sometimes the ceilings and walls of a room are of such 
shape that a person standing in a certain position may dis- 
tinctly hear all that is said by another person at a distance 
in some other part of the room, though speaking in but a 
faint whisper. The shape of the ceilings or walls is such 
that all the sound-waves reflected from different parts are 
brought by reflection to the place where the first person 
is standing. This frequently happens in rooms with dome- 
shaped ceilings. The name whispering galleries is given to 
such rooms. 

In the dome of St. Paul's in London, persons standing on opposite 
sides of a gallery, extending around the inside of the dome, may con- 
verse in faint whispers. The person talking places his mouth near the 
wall ; the one listening holds his ear near that portion of the wall 
directly opposite. 

238. Refraction of Sound. — The rectilinear direction 
in which sound-waves move is changed, when the waves 
pass from one medium into another of different density. 
In this case, the direction of the waves is changed at the 
surface of the dense medium, but the waves, instead of 
being thrown off or reflected by the medium, pass through 
the dense medium, in a direction different from that in 
which they were moving, before they reached the new 
medium. The change so caused in the direction of sound 
is called the refraction of sound. Sound is refracted in pass- 
ing from air into water or glass, or in passing from water 
or glass into the air. 

239. The Effect of Distance on Sound. — If we are 

walking towards a distant bell while it is sounding, we 
notice that the sound grows louder as we approach the 
bell. 

The speaking-tubes which connect the different rooms 
in a building, enable a person talking in a moderate tone 
to be distinctly heard by a person listening in another 
li 



162 NATURAL PHILOSOPHY. 

part of the building. Here the intensity of the sound is 
not so greatly diminished, because the sound-waves, con- 
fined to the air in the tube, move in one direction only, 
and do not spread outwards in all directions. For the 
same reason, the faint sounds conveyed by the string or 
the wire in the string-telephone are distinctly heard at 
the other end. 

Experi ment 49 . — Speak faintly into an empty water hose. Observe 
the fact that a person listening at the other end can hear distinctly what 
is said. 

«K>>@<OC 

Problems. 

1. A piano string is vibrating with a frequency of 256 vibra- 
tions per second. What will be the frequency, if the string be 
shortened to J and J of its length respectively, the stretching 
weight remaining the same? Arts. 512, 768. 

2. Under favorable conditions a powerful human voice may be 
heard in the open air a distance of 700 feet. Assuming the tem- 
perature of the air to be 60° F., what time will be required to 
transmit the sound of any syllable? Ans. 0.625 second. 

3. What time will be required to transmit the above sound if 
the temperature of the air is 32° F. ? Ans. 0.642 second. 

4. A distant man is seen to strike a blow with a hammer. Four 
seconds elapse before the sound of the blow reaches the ear of the 
observer. What distance is the man from the observer, if the 
temperature of the air is 70° F. ? 

Ans. 4524 feet (approximately). 

5. A lightning flash is observed to strike a distant object, six 
seconds before the thunder is heard. What is the distance of the 
object from the observer, the air being at the temperature of 
60° F.? Ans. 6720 feet. 

6. A person standing before a distant cliff, on shouting dis- 
tinctly, hears an echo of two syllables. What is approximately 
the distance of the cliff, the temperature of the air being 60° F. ? 

Ans. 224 feet. 




CHAPTER XIII. 

THE CHARACTERISTICS OF MUSICAL SOUNDS. 
MUSICAL INSTRUMENTS. 



-^o>©<o 



240. Musical Sound and Noise. — The vibrations of 
sounding bodies produce a variety of sounds. These, gen- 
erally speaking, may be divided into musical sounds and 
noises. All sounds, whether musical or noisy, consist of 
various combinations of simple, musical sounds. 

Musical sounds are characterized by smoothness and 
regularity. When this smoothness and regularity are 
absent, noises are produced. 

Noises may be divided into : 

(1.) Continuous Noises, or those produced by the simul- 
taneous occurrence of a number of discordant musical 
sounds, as when several consecutive keys on a piano are 
struck simultaneously. 

(2.) Momentary Noises, or those produced by the simul- 
taneous occurrence of a number of sounds that continue 
for too short a time to permit their pitch to be recognized 
by the ear, as in the report of a gun. 

The unpleasant effect produced on the ear by noises, may be com- 
pared to a similar effect produced on the eye by a flickering light. In 
both cases, the unpleasant feeling is probably caused by the sudden and 
abrupt changes transmitted by these organs to the brain. 

241. Musical Sounds Produced by Regular Im- 
pulses. — That successive impulses will produce musical 

163 



164 NATURAL PHILOSOPHY. 

sounds, when they follow each other with sufficient rapid- 
ity, is a matter of common experience. As the teeth in 
a circular saw successively strike the board it is sawing, a 
musical sound is produced. 

Experiment 50.— Draw the blade of a pen-knife over the milled 
edge of a large coin ; if the motion is sufficiently rapid, the separate taps 
will produce a musical tone. 

242. The Characteristics of Musical Sounds. — 

Although musical sounds may differ in a great variety of 
ways, yet these differences may all be traced to three pe- 
culiarities or characteristics ; viz., the intensity or loudness, 
the tone or pitch, and the quality or timbre, 

243. Intensity. — By the intensity of a sound is meant 
that peculiarity which enables us to distinguish between 
a loud and a feeble tone. 

When a bell is struck vigorously, it emits a loud sound, 
because the distance through which its sides swing is com- 
paratively great, and the air around the bell is consider- 
ably condensed and rarefied. 

Experiment 51. — Stretch a wire firmly between two stout hooks, 
securely fastened to the top of a table. Pluck the wire gently with the 
fingers : a musical sound will be heard. Now pluck the wire at the same 
point, but with more force, and observe that a note will be heard louder 
than before, but neither higher nor lower in pitch. The two notes are 
of the same pitch, but they differ in their intensity or loudness. 

244. The Speaking Trumpet is a device employed 
to cause the voice to be heard at great distances. It 
is conical in form, and is trumpet-shaped at its larger 
end. The small end is held to the mouth of the person 
talking. 

Experiment 52. — Eoll a piece of stout pasteboard into a cone; 
place the mouth at the small end, and talk or sing into the cone. Observe 
that the sound of the voice will be greatly strengthened. Point the cone 
directly at a person standing at the far end of a room, and whisper ; he 
will be able to hear distinctly all that is said, while those on either side 
of the instrument, though nearer it, are unable to hear. Unless the tube 
is tightly closed at the sides, it will fail to operate properly. 



MUSICAL SOUNDS. 165 

245. The Ear-Trumpet is an instrument employed to 
aid deaf persons in hearing. It acts by concentrating the 
sound of the voice on the listener's ear. The shape of the 
ear-trumpet is similar to that of the speaking-trumpet, 
but the small end is placed in the ear, and the person 
talks into the large end. 

Experiment 53. — Place the small end of the paper cone used in 
the preceding experiment, in a person's ear and whisper into the large 
end ; observe that he will hear much more distinctly than without the 
cone. Go to the far end of the room and again whisper, though some- 
what louder, and he will still hear what is said. 

216. Pitch.— By the pitch of a musical sound is meant 
that peculiarity which enables us to distinguish between 
sounds that are high or low, shrill or grave. 

Pitch depends on the number of vibrations per second 
imparted by the sounding body to the air ; or, in other 
words, on the frequency. The greater the number of vibra- 
tions, the higher will be the pitch of the sound, or the 
shriller the note. Thus, when a circular saw is in mo- 
tion, the more rapid its rotation, the shriller will be the 
sound which it produces. 

A wheel furnished with teeth on its circumference, and supported on 
a suitable frame, as shown in Fig. 90, may be set in rapid rotation by 
means of a cord wrapped around its axis. If now, 
a card be held against the teeth, a musical sound 
will be produced, the pitch of which will be 
shriller the more rapid the rotation. As the 
wheel gradually moves slower and slower, the 
pitch of the note descends in a marked manner. 

The shorter the length of a vibrating 
string or wire, the more rapid its vibra- 
tion ; hence the shriller the notes it Fi s- 90-Savart's 

. Wheel, 

emits. The shrill, treble notes of a piano 

are produced by the short, thin strings ; the grave, bass 
notes, by the long, thick strings. 

After a piano-string has been struck, the sound will 
gradually become fainter, because the string moves 




166 NATURAL PHILOSOPHY. 

through a shorter and shorter distance. The pitch of 
the note, however, will not change, since the frequency 
of the vibration remains the same. 

Experiment 54. — Cut out a bridge or rectangular-shaped piece of 
hard wood, with a flat base and a sharp edge, rather too high to go under 
the wire stretched across the top of the table, as described in experiment 
No. 51. Lift the wire and place the bridge under it so that the wire will 
press firmly against its sharp edge. Observe that on sliding the bridge 
from one end of the wire to the other, the shorter the portion of the wire 
vibrated, the shriller will be the note produced, that is, the higher will 
be its pitch. 

Experiment 55. — Move a moderately long blackboard-crayon, held 
loosely in the fingers, over the surface of a blackboard, so as to produce 
a shrill sound. This sound is caused by a series of taps rapidly follow- 
ing one another. Examine the line made by its motion over the board, 
and observe that it consists of a number of separate marks made each 
time the chalk taps against the board. Alter the pressure of the chalk 
on the board, so as to obtain sounds of different pitch. Examine the 
lines and observe that the shriller sounds were produced by the greater 
number of taps in a given time. 

247. The Limits of the Human Ear. — The limits of 
hearing vary in different persons. No one, however, can 
hear sounds produced by less than 16 complete vibra- 
tions per second, or by more than about 48,000 per second. 
If the vibrations are less than 16 per second, we hear each 
separate tap or blow ; if they are more than about 48,000, 
the sound becomes too shrill to be audible. 

248. Methods of Determining Pitch. — The pitch of 
a musical tone may be determined : 

(1.) By the siren. 

(2.) By Savart's toothed wheel. 

(3.) By some graphic method. 

249. The Siren. — The siren consists practically of an 
air turbine, driven by the pressure of streams of air 
directed through fixed guides, causing the rotation of a 
plate containing orifices through which the air-streams 
escape. 



MUSICAL SOUNDS. 



167 




Pig, 91 -The Siren. 



A sectional view of the siren is shown in Fig. 91. The cylinder 
A, is mounted on a wind-chest. At the upper end of the cylinder 
is fixed a smooth, metallic plate B. Immedi- 
ately above this plate is a movable plate (7, at- 
tached to an axis D, which permits it to move 
freely over the plate B. Both B and C, are 
pierced at regular intervals with small holes, ex- 
tending through the plates in an oblique direc- 
tion, as shown in the figure. The holes in B, are 
equal in number to those in C, but are inclined 
in the opposite direction. 

When a current of air is forced through the 
cylinder A, the plate C, and the axis to which it 
is connected, are set in rapid rotation, and a mu- 
I sical note is produced whose pitch increases as 
I the speed of rotation becomes greater. This note 
is caused by the puffs of compressed air that, at 
t regular intervals, are allowed to escape through 
; the openings of the plate B, when they are not closed by the plate C. 
* The number of columns of compressed air that escape in this manner 
will "depend both on the number of openings in the plate B, and on the 
i speed of revolution of the plate C. 

% To determine the number of revolutions of (7, an endless screw H, 
attached to the axis D, moves counters (like those on gas-meters), over 
' graduated dials, by means of the toothed wheels and I. 

In order to use the siren to ascertain the pitch of any note, wind is 
i urged through the cylinder A, until the pitch of the note given by the 
i siren is the same as that of the note, the number of whose vibrations is 
J to be determined. The speed of the siren is now kept constant, and the 
1 number of revolutions of the plate during any second ascertained. The 
j number of revolutions multiplied by the number of openings in the 
"} plate B, will give the number of vibrations per second required to 
i produce the given note. 

250. Savart's Toothed Wheel, Fig. 90, when used to 
^determine the pitch of a musical note, is provided with a 
^counting device similar to that placed on the siren. The 

'number of vibrations required to produce the note is de- 
termined by multiplying the number of revolutions of 
jthe wheel by the number of teeth. 

251. Graphic Method. — If a stylus or point be at- 



168 NATURAL PHILOSOPHY. 

tached to one of the prongs of a tuning-fork F, and the fork, 
while sounding, be moved over the lampblack-coated sur- 
face of a glass plate A, Fig. 92, a sinuous or wavy line 
will be produced as shown. Since each wave is 
produced by one complete to-and-fro motion of 
the fork, it is evident : 

(1.) That if the time required to draw the fork 
over a given length of the plate is known, the 
number of vibrations performed in that time may 
be directly determined by counting the number 
of elevations and depressions in the sinuous line. 
Such an apparatus is called a phonautograph. 
(2.) That if the number of vibrations produced 
by the fork, in a second, is known, the time re- 
quired to draw it over the plate, through a dis- 
tance equal to an elevation and depression may 
be determined. Thus, if the fork makes 1024 
Pig, 92. vibrations per second, a very small fraction of a 
^term?- secon d ma y be measured, since the fork makes 
nation of one complete vibration in the ToV^h °f a second, 
1 c ' and if the motion be sufficiently rapid, the dis- 
tance may be readily divided into hundredths or thou- 
sandths. 

Such an apparatus is called a chronograph. 

252. Quality or Timbre. — When the same note is 
sounded with equal loudness on two different musical 
instruments, as on a piano and on a flute, although the 
notes are of exactly the same pitch and intensity, yet 
there is something which enables the ear to distinguish 
one note from the other. Or, when two persons are speak- 
ing in the same tone, we can recognize a difference in the 
sounds produced ; these peculiarities are known as the 
quality of the sounds. 

253. Fundamental Tone of a String. — When the 
tightly stretched wire or string a b, Fig. 93, is caused to 




MUSICAL SOUNDS. 169 

vibrate transversely as a whole, it produces the lowest or 

gravest tone it is capable of producing. This tone is 
called its fundamental tone. 



Fig. 93.— Fundamental Tone of String. 

254. Overtones or Harmonics of a String. — It is 

difficult to make the string shown in Fig. 93, vibrate only 
as a whole. There is a tendency for the string at the same 
time to divide itself into a number of shorter parts, which 
produce additional tones called overtones. These overtones 
are shriller than the fundamental tone, as the lengths of 
the parts into which the string is divided are smaller than 
the entire length. 

In the notes of all musical instruments, overtones accompany the fun- 
damental tone, and impart to the tone its pecular quality or timbre. 
The different overtones are of unequal intensity or loudness in differ- 
ent instruments. 

In some instruments the overtones produce pleasing chords with the 
fundamental tone. In such cases the instruments produce brilliant, 
pleasing tones. In other instruments, however, the overtones produce 
discords with the fundamental. In these cases the tones produced are 
flat, harsh, and unpleasant. 

Some pianos produce more brilliant tones than others because the 
strings are so struck as either to prevent altogether the formation of 
objectionable overtones or greatly to decrease their intensity. 

255. Sympathetic Vibrations. — 

Experiment 56.— Suspend a weight of 10 or 15 lbs. by a string, 
and let it swing as a pendulum. Note the time of its oscillation. Now, 
while it is swinging very gently, blow a puff of air against it from the 
mouth, just as it is moving away. Wait until it is again moving away, 
and give it another puff of air. Do this thirty or forty times and ob- 
serve the fact that the pendulum will acquire a considerable increase of 
motion. 

While the pendulum is swinging freely, give it the puffs of air when it 
is just beginning to move toward you, and the motion will be stopped sooner 
than otherwise. 

P 



170 NATURAL PHILOSOPHY. 

Experiment 57. — Partially raise the top of a piano, and place the 
foot on the loud pedal ; lean over the instrument, and sing any note into 
it, in a loud voice. On ceasing to sing, observe that the same note is 
given back by the piano. Now sing a different note, and observe that 
the piano will give back this particular note ; and so with any other note 
sang into it. The sound-waves produced by the voice have struck against 
all the strings of the piano, but have only set in vibration those particular 
strings that are capable of giving sounds of the same pitch as their own. 
Vibrations so produced are called sympathetic vibrations. 

The cause of sympathetic vibrations is as follows : the 
sound-waves strike all the strings, and give each a very 
feeble push. If the time of vibration of any string be 
exactly the same as the time of the vibration of the sound 
wave striking it, the next forward impulse which the waves 
give to the string will be received just as it is beginning 
to move forward, and hence the motion acquired by the 
first impulse is increased by the second impulse, and as 
the same is true of all the other impulses, the string 
eventually acquires considerable motion, and emits an 
audible sound. If, however, a string has a rate of motion 
different from that of the sound-waves, it will sometimes 
receive a forward impulse from the waves when it is 
moving in the opposite direction, and its motion being 
thereby diminished, it can never acquire any consider- 
able motion. 

256. Examples of Sympathetic Vibrations. — If 
various powerful notes be sung, or otherwise produced, 
near a table on which a number of goblets and glasses of 
different sizes are placed upright, when the proper note 
is struck, one of the goblets or glasses will be set into 
sympathetic vibrations and will emit this note. 

The gas-lights in a ball-room have been known to vary 
rhythmically in height, in unison with the music of the 
orchestra, when certain notes were sounded. 

257. Resonance. — We have already seen how the voice 
of a speaker may be strengthened by the reflection of 
sound-waves from the ceiling and walls of a room. 



MUSICAL SOUNDS. 



171 



A mass of air whose dimensions are such as to enable 
it, when set in motion by any sound, to vibrate in ex- 
actly the same time as that sound, will greatly increase 
its intensity by what is called resonance. Resonance of 
this kind is, therefore, dependent for its action on sym- 
pathetic vibrations. 

The strings of a violin or guitar have too small a surface to set much 
air in motion. The notes produced by these instruments are greatly 
aided by the vibrations of the wood forming the body of the instru- 
ments. It is on the elasticity of the wood, and its ability to accept dif- 
ferent rates of motion from the strings, that the musical value of the 
instrument depends. This appears to increase with the age of the 
wood, and the number of times the instrument has been used. 

Experiment 58. — Stretch a wire across the corner of a room to the 
walls, pluck it and observe the note it gives. Now stretch it when 
attached to hooks in the top of a table and observe that it gives a much 

aore powerful sound, because the table now takes up the motion of the 

rire much better than do the walls of the room. 

In order to increase the intensity of the overtones of a 
note sufficiently to enable them to be distinctly heard, 
instruments called resonators are employed. Resonators 
consist of hollow spheres of brass, as shown in Fig. 94, 
with openings at a and b ; one of 
these a, is placed in the ear, and at 
the other the sound-waves enter. If 
there is present in any tone an over- 
tone whose rate of vibration is ex- 
actly the same as the rate in which 
the air contained in the sphere can 
ibrate, the resonance of the sphere will cause this over- 
3ne to be distinctly heard. 

The resonant case on which a tuning-fork is mounted, 
should contain a column of air whose rate of vibration is 
exactly that of the fork. 

Across the far end of the tube or alley-way leading from 
the outside of the ear inwards, is a tightly stretched drum- 
head, or closed gate, called the tympanum. The column of 




Fig, 94,— Resonator, 



172 



NATURAL PHILOSOPHY. 



air contained within this tube is capable of resounding to 
and greatly strengthening certain sounds by resonance, as is 

partially illustrated 
by the following 

Experiment 59. — 

Tie two strings to a 
poker, or to a bar of 
steel or iron, some little 
distance from the ends, 
as shown in Fig. 95. 
Hold the ends of the 
string over the end of 
one of the fingers of each 
hand, letting the poker 
hang in a horizontal po- 
sition. Now insert in 
the ears the fingers hold- 
ing the strings, being 
careful that the strings 
do not rest against the 
body. Let some one 
strike the poker near 
the middle, and observe 
that a sound will be heard 
like that of a large bell 
when you are very near it. 
Here the vibrations of 
the poker are transmitted through the strings to the columns of air 
within the ears, which by resonance strengthen the sound. The effect 
is also due to the vibrations being carried through the bones of the head 
directly to the ear. 

The air which fills any hollow body will resound to some 
particular note. When a shell is held close to the ear a 
sound is heard, which a pretty superstition of childhood 
regards as the imprisoned sounds of ocean waves beating 
against a shore. The sounds are caused by the air with- 
in the shell strengthening, by its resonance, the feeble 
sounds that are always present in the air. Similar sounds 
may be heard by holding an empty pickle-jar or tomato- 
can near the ear. 




Fig, 95,— An Experiment in Resonance. 



MUSICAL SOUNDS. 



173 



Experiment 60. — Punch a hole in the bottom of an empty tomato- 
can. Eun a stout string through the hole and knot the string at the 
end to prevent its being pulled out. Holding the can in the hand, as 
shown in Fig. 96, run the ros- 
ined fingers down the string, 
and observe the fact that a 
noise far from musical will be 
heard. The vibrations of the 
string are strengthened by the 
resonance of the air within 
the can. 

Try the same experiment 
with a shorter can, and it 
will be found to give a much 
shriller note. 

258. The Interfer- 
ence of Sound Waves. 
— When two notes of 
the same intensity and 
pitch are simultane- 
ously sounded, they 
sometimes strengthen, 
and sometimes partly or 
completely obliterate each 

n fi iPr Fig- 96.— An Experiment in Resonance. 

When two separate notes are sounded together, if the 
waves of one of the notes condense the air at the same 
time that the waves of the other note are condensing it, 
the air will be more condensed. The amplitude of the 
resulting wave will be greater, and the sound will, there- 
fore, be louder. 

If, however, the waves of the one note condense the air 
at the same time that the waves of the other note are 
rarefying it, and the amplitude of each set of waves is 
equal, the air will be neither condensed nor rarefied and 
silence will result. If the amplitudes of the two sets of 
waves are not equal, a sound will be heard less intense 
than either of the two sounds. These effects are known 
as the interference of sound. 




174 NA TUBAL PHILOSOPHY. 

259. Beating. — When two notes of nearly but not ex- 
actly the same pitch are simultaneously sounded, a pecu- 
liar throbbing or palpitating sound, alternating in strength 
and feebleness, is heard. This effect is known as beating 
and is due to the interference of two sounds. At cer- 
tain times, both sounds are condensing or rarefying the 
air simultaneously, while at other times one sound is con- 
densing the air while the other is rarefying it. Hence the 
alternations in strength and feebleness. 

When the beats follow one another too rapidly, they cease to be 
heard distinctly, and merely cause an appreciable roughness in the two 
sounds. When a certain rapidity is reached, the beats cease to be heard. 

Two notes of nearly the same pitch, when sounded separately, are 
with difficulty distinguished, but when sounded together, the differ- 
ence in their pitch is at once recognized from the resultant beating. 
This principle is utilized in tuning an instrument. The note is judged 
to be in unison with a standard tuning-fork or pitch-pipe, when the 
two can be simultaneously sounded without beats being heard. 

260. Musical Instruments. — Musical instruments 
may be divided into three classes : 

(1.) Stringed instruments. 
(2.) Wind instruments. 

(3.) Instruments in which the sounds are produced by 
the vibration of plates or membranes. 

261. Stringed Instruments are those in which sounds 
produced by the vibrations of strings are suitably inten- 
sified by resonance. Examples of stringed instruments 
are seen in the piano, the harp, the violin, the violoncello, 
the guitar, and the banjo. In the piano and the harp 
there is a separate string for each note. In each of the 
other instruments, the same string is made to give differ- 
ent notes, by pressing it at different points with the finger, 
and thus practically shortening its length. The tighter 
any string is stretched, the shorter the length of the 
string, and the smaller its diameter, the shriller the note 
which it will give. 



MUSICAL SOUNDS. 175 

262. Wind Instruments are those in which sounds 
are caused by the vibrations of a column of air contained 
within the instrument. The pitch of the notes depends 
upon the dimensions of the air-column, and upon whether 
the tube containing the column of air is open at both 
ends, or at but one end. 

The column of air in a wind instrument may be set into 
vibration in a number of ways, of which the most import- 
ant are : 

(1.) By means of a mouth-piece, 

(2.) By means of a vibrating plate called a reed. 

In the organ-pipe, the vibrations of the air-column are 
produced by the action of a mouth-piece. The organ-pipe 
is placed on a box called the wind-chest, supplied with air 
from a bellows. The air entering through the opening a, 
Fig. 97, passes through a narrow slit c, and escapes at the 
opening o. 

A reed is a thin, vibrating plate of any elastic material, 
which is moved backwards and forwards by the air. The 
notes of reed-organs, accordions, and jews-harps are caused a 

by the vibrations of reeds. Fig. 97. 

An Organ- 

Experiment 61 . — Cut a stout wheat straw into a length Pipe, 
of about four inches from the knot. With a sharp pen-knife 
cut a slit a, down the side of the knot b, as shown in Fig. 98. Now place 
the mouth completely over the cut part and blow, and observe the musical 



Fig. 98 —A Straw Eeed. 

note that will be produced. The pitch of this note will increase, if the 
length of the straw tube is shortened by cutting a piece off the open 
end. 

Experiment 62. — Prepare a straw reed as before, but use a larger 
straw, and cut holes in the side about one inch apart. Sound the reed 
when the holes are all open, and remember the pitch of the note. Now, 
with one finger close the hole nearest the knot end, and observe that the 
pitch of the note produced will be lower ; close the next hole, still keep- 
ing the finger on the opening previously closed, the note will be still 
lower. These effects are the same as would be produced by lengthening 
the pipe. 



176 NATURAL PHILOSOPHY. 

In the flute, the flageolet, and the fife, the different 
notes are produced by virtually altering the length of 
the air-column by opening or closing holes in the side of 
the instrument. 

263. Vibrating Plates and Membranes. — In the mu- 
sical box, the notes are produced by the vibrations of a 
series of steel teeth of different lengths, which are set 
into motion by pins projecting above the surface of a 
revolving cylinder. 

In the xylophone, the notes are produced by the vibra- 
tions of plates of wood of different lengths. The notes 
of the cymbal are produced by the vibrations of brass 
plates ; those of the drum, by the vibrations of a mem- 
brane. 

264. The Phonograph, an invention of Edison, is a 
device for recording sounds and reproducing them at any 
future time. The principle of its operation consists essen- 
tially in causing a cutting point, attached to the centre of 
a flexible diaphragm, moving up and down under the in- 
fluence of a speaker's voice, to leave on the surface of a 
rotating cylinder of hardened wax, a permanent record of 
the movements of the diaphragm, and of using such in- 
dentations to reproduce in the same diaphragm, the mo- 
tions that caused them. 

The construction of the Phonograph is shown in Fig. 99. A metal 
cylinder is rotated on the axis A B, by means of an electric motor 
placed inside the box support at B, through a belt passing over a pul- 
ley P. A flexible diaphragm D, clamped at its edges, and provided 
with a cutting point attached at its centre, is so supported, that on the 
rotation of A B, it moves lengthwise on the axis A B. 

In order to record the sounds of the voice, a hollow cylinder of hard- 
ened wax C, is slipped over the horizontal axis A B, and the cutting 
point on the diaphragm brought in contact with it, near one end. On 
the rotation of the cylinder, a continuous spiral is cut on the surface of 
the cylinder. Tf now, during its operation, the mouth-piece M, attached 
to a flexible rubber tube T, is fixed to the end of the diaphragm D, 



MUSICAL SOUNDS. 



177 



removing the rubber tube shown in the figure for this purpose, a per- 
son talking into M, will cause the diaphragm D, to cut indentations in 
the wax surface, the number of which will depend on the frequency of 
the sound-waves produced by the speaker' s voice. 




Fig. 99— The Phonograph, 

To cause the phonograph to reproduce the speech, the same dia- 
phragm is employed, but the sharp cutting point is replaced by a blunt 
point. The wax cylinder is placed under the point, at the begin- 
ning of the record, and revolved by the motor. As the blunt point 
attached to the diaphragm follows the minute elevations and depressions 
cut in the surface of the wax, movements are imparted to the diaphragm 
exactly similar to those produced by the voice of the speaker. Conse- 
quently, a person listening at the diaphragm can distinctly hear all that 
was originally spoken against it. In the figure, a flexible rubber tube, 
provided with ear-pieces E, E, is shown attached to the diaphragm at D. 

12 




CHAPTER XIV. 

LIGHT— ITS NATURE AND CAUSES. 
«x>>^o* 

265. The Nature of Light. — Light is caused by a 
wave motion in an extremely tenuous medium called the 
luminiferous ether. The bell rung in the empty vessel, 
shown in Fig. 87, cannot be heard, because in the vessel 
there is no air to be set into waves. The carbon thread 
of an incandescent electric lamp, though placed in a glass 
vessel from which nearly all the air has been removed, 
readily sends its light across the space within the vessel. 
The light of the sun and stars reaches the earth across the 
apparently empty space which exists between these bodies 
and the earth. 

266. The Luminiferous Ether fills all space, even 
that between the adjacent molecules and atoms of matter. 
The space occupied by the atoms is alone believed to be 
free from the ether. 

267. Light and Sound Waves. — Light, like sound, is 
an effect produced by wave motion. The waves producing 
sound, however, are set up in a gross medium, the air, 
while those producing light are set up in a tenuous me- 
dium, the luminiferous ether. Moreover, the vibrations of 
sound are longitudinal ; that is, the particles of air move 
to-and-fro in the same direction as that in which the sound 

178 



LIGHT— ITS NATURE AND CAUSES. 179 

waves are advancing, while the vibrations which produce 
light are transverse, that is, the ether moves at right 
angles to the direction in which light-waves are advancing. 

268. The Undulatory Theory of Light assumes that 
light is due to waves or vibrations in the luminiferous 
ether. By means of these waves, light and energy are 
transferred from one place to another. The transfer of 
energy by means of ether waves is called radiation. 

Ether waves have been measured whose frequency is as high as about 
forty quadrillions (40,000,000,000,000,000) of double or complete vibra- 
tions per second. Besides these there are waves whose frequencies are 
much lower. Those having a frequency between 392 trillions and 757 
trillions, possess the power of affecting the eye and producing the sen- 
sation of light. Since the frequencies of the ether waves are so great, 
their wave lengths must be extremely small. 

Ether waves of any frequency, striking ordinary matter, 
may. produce in it the phenomena of heat; or, when fall- 
ing on a sensitized photographic plate, or on the leaf of a 
growing plant, may produce therein a chemical decompo- 
sition. This latter effect is called an actinic effect. 

In either of these cases the waves of light, falling on matter, produce 
therein a to-and-fro motion of its molecules. When luminous effects 
are produced, these to-and-fro motions are of a frequency sufficiently 
great to affect the eye. In the case of the photographic plate, or of 
the leaf, the to-and-fro motions are sufficiently great to produce a de- 
composition of the molecules ; in the case of heat, they warm the body. 

There are, therefore, three classes of effects which ether 
waves may produce on ordinary matter; namely, heat- 
ing effects, luminous effects, and actinic effects. 

269. Double Meaning of the Word Light.— The 
word light, like the word sound, is used in two distinct 
senses : 

(1) As the cause which produces the sensation ; viz., 
the ether waves of the necessary frequency. 

(2) As the sensation produced in the mind through 
the intervention of the eye. 



180 NATURAL PHILOSOPHY. 

270. Sources of Light. — The principal sources of light 
are the sun and the fixed stars, chemical combinations, 
and electricity. Nearly all the earth's light comes from 
the sun. Artificial light is obtained from a variety of 
sources, the principal of which are combustion and elec- 
tricity. 

271. Luminous and Illumined Bodies. — A body 
which produces the light it gives off is called a luminous 
body. A lighted candle is a luminous body, since it pro- 
duces the light which it emits. A body which shines by 
throwing off light it has received from a luminous body, 
is said to be illumined. The sun is a luminous, and the 
moon an illumined body. Nearly all visible bodies are 
illumined ; we see them by means of the light they re- 
ceive from luminous bodies. 

272. Transparent, Translucent, and Opaque Bod- 
ies. — A transparent body allows light to pass through it 
in such a manner that we can see clearly through it the 
outlines of other bodies ; water is transparent. 

A translucent body allows light to pass through it in 
such a manner that we cannot see through it the outlines 
of other bodies ; oiled paper is translucent. 

An opaque body does not allow any light to pass 
through it; iron and wood are opaque. 

The difference between a transparent and a translucent 
body does not consist in the amount of light which passes, 
but in the manner in which the light passes. 

Many substances that are opaque when in fairly large masses are par- 
tially transparent when in thin films ; thus, a film of gold is transparent 
to yellowish-green light ; a film of silver is transparent to a bluish light. 

A transparent substance permits luminous or illumined 
bodies to be clearly seen through it, because it does not 
change the direction of the rays of light which such 
bodies emit. A translucent body will not permit such 
bodies to be seen through it because it changes the direc- 



LIGHT— ITS NATURE AND CAUSES. 181 

tion of the light which passes through it. As the light 
comes out of the translucent body, it is scattered or dif- 
fused in all directions, so that only the surface of the 
translucent body is seen. 

273. Ray, Beam, and Pencil. — A ray is a single line 
or path of light, taken in the direction in which the light 
is moving ; a beam is a number of parallel rays ; a pencil is 
a number of converging or diverging rays. A pencil of 
light is converging when the rays are all moving towards 
the same point ; and diverging, when they are all moving 
from the same point. 

274. How Bodies become Visible. — Only those 
bodies are visible which throw off light in all directions. 
Both luminous and illumined bodies are, therefore, visible. 
A body which regularly reflects light cannot be seen. A 
clean, plane mirror, placed in a doorway, cannot be seen, 
and may be mistaken for an open doorway. Ordinary 
mirrors are visible by reason of the light diffused from 
their tarnished or dusty surfaces. 

A ray of light is invisible unless it enters the eye. We cannot see 
the rays which pass from the stars to the earth. The path of a ray 
through a dusty room is visible because the particles of dust in the air 
scatter or diffuse the light. 

275. Direction in which Light Moves. — Light, like 
sound, moves in straight lines, provided the medium through 
which it is passing remains the same kind, and does not 
change in density. 

That light moves in straight lines is evident from the following con- 
siderations : 

(1.) When a beam of light comes into a darkened room, it lights up 
the dust particles floating in the air ; we can then see that it moves in 
straight lines. 

(2. ) The shape of a shadow depends on the shape of the body which 
casts it ; this could only happen by the light moving in straight lines. 

(3.) If an opaque body be held between the eye and any visible ob- 
ject so as partly to hide it, the parts remaining invisible will be sepa- 

Q 



182 



NATURAL PHILOSOPHY. 



S 



rated from the visible parts by a line of the same general shape as the 
edge of the interposed body ; the rays of light have evidently passed 
over the edge of the interposed body in straight lines and have not been 
sensibly bent around it. 

(4. ) We point a gun directly at a mark, allowance being made for the 
wind and drop of the ball, because we assume the rays of light pass 
directly from the mark to our eyes in straight lines. 

276. Intensity of Illumination. — Law of Inverse 
Squares. — Let S, Fig. 100, be a luminous point, and A, 
B, and Z>, square screens, one inch, two inches, three 
inches and four inches in length of side, 
respectively. Then it is evident that A, 
one square inch in area, will receive the 
same quantity of light as B, which has 
four square inches in area, (7, which has 
nine square inches, or D, which has six- 
teen square inches. Consequently, the 
amount of light which falls on each square 
inch of surface is one-sixteenth at Z>, one- 
ninth at 0, and one-fourth at B, of that 
which falls on A. That is to say, the illu- 
mination of the surface A, is four times 
that of J5, nine times that of (7, and six- 
teen times that of D. But if A, is one foot 
from S, B, is two feet, (7, three feet, and D, 
four feet. Consequently, the illumination of a 
surface from a point source of light varies in- 
versely as the square of the distance between 
them. 

If the light emitted by S, is doubled, that 
falling on all the plates will be doubled. If the light 
emitted by S, is halved, that falling on all the plates will 
be halved. Consequently, the illumination of a surface by a 
point source, varies directly with the luminous intensity of the 
source. 




Fig. 100 —The 
Law of Inverse 



277. Photometers. — The luminous intensity of differ- 



LIGHT— ITS NATURE AND CAUSES. 183 

ent sources of light is measured by means of instruments 
called photometers. 

A clean grease spot on a sheet of paper becomes visible 
when held between the eye and a source of light, because 
more light comes through the greased spot than elsewhere. 
When viewed by reflected light it appears darker than the 
rest of the paper, because less light is thrown off from it. 
If held between two sources of light, so that the paper is equally 
illumined on each side, the grease spot will disappear, since it 
will then be no brighter than the rest of the paper. If 
the paper be moved towards either light, the spot will 
again appear. This is the principle of Bunsen's Photometer, 
in which a grease spot is made in a sheet of paper sup- 
ported in a frame. The paper is placed between two 
lights, and moved backwards and forwards until a posi- 
tion is obtained at which the spot disappears. Call the 
two. lights A and B, and suppose the screen to be one foot 
from A, and two feet from B, then B, has four times the 
luminous intensity of A. 

278. Standard Candle. — Candle Power. — In order 
to compare the intensity of different sources of light, a 
standard of comparison, such as a standard candle, is 
adopted. A standard candle is the intensity of light 
given out by a candle of given purity of composition, 
that will burn at the rate of 120 grains per hour, or 2 
grains per minute (0.1296 gramme per minute). 

In photometric measurements the intensity of the light to be meas- 
ured is obtained in terms of a standard candle. The number of stand- 
ard candles or fractions thereof, that it equals, is called its candle power. 

279. Images Formed by Small Openings. — If the 

light from brilliantly illumined objects be allowed to come 
through a small opening into a dark room, and fall on a 
white screen, as in Fig. 101, there will be formed on the 
screen a distinct image of the objects from which it came. 
The image will have the same colors as the object, but its 



184 



NATURAL PHILOSOPHY. 



size will depend on the distance of the screen from the 
opening. 

The diffused light, coming from all points of the object, enters the 
opening and produces on the screen an exact representation of the parts 




Fig, 101.— Images Formed by Small Apertures, 

from which it came. As, however, the rays cross at the opening, the 
light from the top parts of the object will be received on the lower parts 
of the screen, and those of the lower parts of the object, will be re- 
ceived on the top parts of the screen ; the image will, therefore, be inverted. 

Experiment 63.— Allow the sunlight to pass through a hole in the 
shutter of a darkened room, and fall on a piece of white paper held at 
right angles to the direction in which the light is entering the room. 
Observe the round disk of light that will be seen on the paper. This is 
the image of the sun. 

Experiment 64. — Place a smooth piece of tin-foil over the hole in 
the shutter. Punch a hole in the foil with a large pin or needle, and 
allow the diffused light from the trees, houses, or other objects outside, 
to fall on a screen held opposite the pin-hole. Observe the inverted im- 
age of the objects outside that will be seen on the paper. 

Experiment 65. — Unsolder the top from an empty tomato can, by 
holding it in the flame of a Bunsen burner, and punch a hole in the bottom 
with a nail. Paste a piece of tin-foil over the nail-hole, and make a pin- 
hole in it. Cover the open end of the can with a piece of oiled paper. 
Bring a lighted candle near the pin-hole and observe the inverted image 
of the candle that will be seen on the paper. 



LIGHT— ITS NATURE AND CAUSES. 



185 



280. Shadows. — When light falls on an opaque body, 
the space immediately behind the body, into which no 
light penetrates, is called a shadow. 

Shadows result from the fact that light moves in straight 
lines, and is not perceptibly bent on passing the edges of 
opaque bodies. 

If a luminous point s, Fig. 102, be placed near an opaque 
body A, the light falling on the opaque body will illumine 




Fig. 102.— Umbra or Complete Shadow 



the parts nearest it, but, grazing the edges of the body, as 
at a and 6, the light will continue moving in sensibly 
the same straight lines, s a and s 6, in which it came from 
the luminous point. If the luminous point come nearer 
the opaque body, as at s', the shadow becomes larger, be- 
ing now bounded by the lines s' a d and s 1 b b'. The shape 
of a shadow, therefore, is dependent on the shape of the 
opaque body, and the size of the shadow on the distance of 
the luminous point from the opaque body. 

When the luminous body has an appreciable surface, 
as £, Fig. 103, the light from its central parts casts a 




Fig, 103.— Penumbra or Partial Shadow. 



shadow of the same shape as before. Only a part of 
this shadow, however, is complete ; viz., that lying within 



186 NATURAL PHILOSOPHY. 

the conical space a o b. As we pass from P P, outside 
this space, the shadow is less complete, since these por- 
tions are illumined by the light coming from the edges 
c d, of the luminous body. That part of the shadow 
lying within a o 6, into which no light penetrates, is 
called the umbra or complete shadow; that lying without 
these lines, as far as af and b g, is called the penumbra 
or partial shadow. 

Experiment 66. — Hang a wet sheet from the ceiling or preferably 
in an open doorway, so to act as a curtain or screen. Place a lighted 
candle on the floor back of the sheet, and then walk backwards and for- 
wards between the sheet and the candle, and observe the curious and 
grotesque shadows that appear to those on the other side of the sheet. 
While walking toward the candle, the shadows rapidly increase in size, 
and, while walking away from it, rapidly decrease. By stepping over 
the candle, the shadows appear to be leaping through the ceiling. 

281. Velocity of Light. — Light moves with the enor- 
mous velocity of about 186,000 miles (300,000 kilometres) 
a second. This velocity would, in one second, carry light 
over a distance greater than seven times around the earth 
at the equator. For all distances on the earth at which 
objects are visible, we may, therefore, regard the trans- 
mission of light as instantaneous. 

The velocity of light has been determined by various astronomical 
observations. It has also been measured on the earth by different in- 
struments especially contrived for the purpose. 

The velocity of light varies with the nature of the medium. In 
water, the velocity is about 140,000 miles per second, and in glass, 
about 125,000 miles per second. 

282. Actions which Take Place at the Surface of 
Bodies. — When light falls on a body, it either passes 
into the body, or is thrown off from its surface. 

The light which is thrown off from the surface is either 
diffused or is reflected. 

The light which passes into a body may pass through 
it, if the body be translucent or transparent. In this 
case, the direction of the light is changed on entering the 



LIGHT— ITS NATURE AND CAUSES. 187 

body, and the light is said to be refracted. When the light 
which enters the body does not pass through it, the light 
is said to be absorbed. 

283. Diffusion of Light.— When the light which falls 
on the surface of a body is thrown off from it in all direc- 
tions or irregularly reflected, it is said to be diffused. Illu- 
mined bodies shine by means of the diffused light which 
they throw off in all directions. 

Bodies become visible by means of diffused light. 

284. Absorption of Light.— Ether waves that are ab- 
sorbed by a body, usually cause its molecules to vibrate 
so as to produce heat. They sometimes causes the mole- 
cules to vibrate rapidly enough to produce light, in which 
case the body is said to be phosphorescent. 

When a surface absorbs most of the light which falls 
on it, the surface appears black or dark, because it dif- 
fuses but little light. No surface absorbs all the light 
which falls on it, since we know of no bodies so black 
as to be invisible. 

285. Phosphorescence. — Phosphorescent bodies are 
those, that when exposed to a bright light, will continue 
to shine for some time after they are taken into the dark. 
The ether waves, in being absorbed, impart their motion 
to the molecules, and cause them to vibrate so as to give 
out light or become luminous. 

The faint light emitted by glow-worms, fire-flies, and jelly-fish, or by 
decaying animal and vegetable substances is sometimes called phospho- 
rescence. This is quite different from the phosphorescence just de- 
scribed, and is due to the slow oxidization of a substance produced by 
the animal, or which results from the decomposition of decaying animal 
or vegetable matter. 




CHAPTER XV. 

THE REFLECTION OF LIGHT. 

286. Reflection of Light.— When light falls on the 
surface of a body, and is thrown off from it at an angle 
equal to that at which it strikes the surface, it is said to 
be reflected. 

287. Laws of the Reflection of Light. — 

(1.) The angle of reflection is equal to the angle of incidence. 
Let a ray of light A B, Fig. 104, fall on a reflecting sur- 
face, such as a piece 
of looking-glass, at 
the point B. At this 
point draw the per- 
pendicular D B, then 
A B D, is the angle 
of incidence, and D B 
C, is the angle of reflec- 
tion. In reflection, 
the light is turned 
out of its straight 
path only at the sur- 
face of the body where reflection occurs. 

(2.) The incident ray, the perpendicular at the point of in- 
cidence, and the reflected ray, all lie in the same plane. 

188 




Fig. 104— Reflection of Light. 



THE REFLECTION OF LIGHT. 189 

Thus, if the incident ray A B, and the perpendicular 
D B, lie in the plane of the paper, the reflected ray B C\ 
will also lie in the plane of the paper. 

288. Amount of Light Reflected. — The amount of 
light reflected at any surface, depends : 

(1.) On the kind of material forming the surface. 

(2.) On the degree of polish of the surface. 

(3.) On the angle at which the light strikes the surface. 

Highly polished metals and glass are excellent reflectors of light. 
Transparent substances, such as glass or water, reflect the greatest amount 
of light the more obliquely the light falls on their surfaces. When 
light falls on such surfaces at nearly right angles, most of the light 
passes through the body. When the sun is nearly overhead, we may 
look at his image in a water-surface without being dazzled, because so 
little of the light is reflected ; but when the sun is nearly setting, the 
image is too dazzling to be looked at steadily. Opaque surfaces, like 
those of polished metals, reflect the greatest amount of light when the 
light falls the most directly on the surface, that is, at right angles to it, 
Considerable light is lost by reflection even from the surfaces of the best 
reflectors. Thus, silver, one of the best reflectors known, reflects about 
90 per cent, of perpendicularly incident light. 

289. Mirrors and Specula. — A highly polished body, 
having a regular surface, and capable of reflecting most 
of the light which falls upon it, is called a mirror or specu- 
lum. A reflector made of glass, or other transparent me- 
dium, covered on the back with some good reflecting 
surface, is called a mirror; a highly-polished metallic 
reflector is called a speculum. Both mirrors and specula 
may be either plane or curved. 

290. Images Seen in Plane Mirrors. — When an ob- 
ject is placed in front of a plane mirror, an image, of the 
same size as the object, will be seen as far back of the 
mirror, as the object is in front of the mirror. 

We always see an image or an object in the direction in 
which the rays of light coming from it enter the eye. If, 
therefore, an object, such as a candle A B, Fig. 105, is 



190 



NATURAL PHILOSOPHY. 




B B' 

Fig. 105.— Images Formed by Plane Mirror. 



placed before the plane mirror CZ), the image will be 
seen by an eye at P, as though the candle were at A' 

B', back of the mirror. 
Every point of the ob- 
ject, as A, sends a cone 
of rays to the mirror, but, 
when reflected, only a 
part of the rays enter 
the eye. This point of 
the image will appear to 
be situated back of the 
mirror where these rays 
apparently meet. 

The image that appears back 
of the glass and which is formed by rays which do not come directly 
from the object, is called the virtual image, because there is no real 
image back of the mirror. The rays of light do not actually diverge 
from the point A / ', but only appear to do so. If the eye looked directly 
at A B, it would see a real image ; that is, one formed by rays coming 
directly from the object. 

Plane mirrors cause the image to appear perverted, that is to say the 
right-hand side of the body appears on its left, and the left-hand side 
appears on the right. 

Experiment 67. — Write on a sheet of paper, and before the ink 
dries, press a piece of clean blotting-paper on the writing, and observe 
that on removing the blotter, it will have a copy of the writing reversed 
from right to left, just as a mirror appears to reverse objects; hold 
the blotter in front of a looking-glass, and the writing on the blotter can 
easily be read in the glass. 

291. Apparent Position of Visible Objects. — No 

object is visible unless all its points give off diverging 
pencils of light. An object looked at directly, is seen by 
means of these diverging rays entering the eye. We see 
the image of an object in a mirror, by means of the diverg- 
ing rays it gives off, which enter the eye not directly from 
the object, but after reflection from the mirror, and each 
point in the image appears to be situated at the point from 



THE REFLECTION OF LIGHT. 



191 



which the visual rays, or those entering the eye, appear to 
diverge. 

The fact that the eye sees an image in the direction in 
which the rays enter it may be amusingly shown as fol- 
lows : 

Experiment 68. — Place four small pieces of looking-glass at a, 6, c 
and d, in the positions shown in Fig. 106. A ray of light from a distant 
object, will, after reflection from 
the mirrors, enter the eye at G, 
in the same direction as that in 
which it came from the object. 
Observe that the eye will see the 
object although an opaque sub- 
stance, such as a brick, be held 
at B, between the eye and the 
object, thus making it appear as 
though the person was seeing 



A 




Fig. 106.— Looking Through a Brick. 



through the brick. The mirrors may be concealed in a suitably shaped 
box, with openings at A and C. 

292. Multiple Images. — When any object is placed 
between two plane mirrors inclined at an angle to each 
other, a number of images will be seen, which will be the 
greater, as the inclination between the two mirrors is less. 
This multiplication of the image of an object is seen in 
the kaleidoscope. 

Experiment 69. — Place two looking-glasses or pieces of glass, at 
any angle with each other, and observe the images of an object placed 
between them. Now change the inclination of the mirrors, and observe 
the change in the number of images. 

293. The Visual Angle. — The rays of light which 
come from opposite extremities of an object, form an 
angle at the eye, called 

the visual angle. We A C 

judge of the size of an 

object mainly by means 

of the visual angle ; the 

larger the visual angle 

the larger the object appears. Thus, in Fig. 107, the 




Fig. 107.— The Visual Angle. 



192 



NATURAL PHILOSOPHY. 



visual angle under which the eye sees the object A A, is 
A A. If, now, the object is carried to A' A r , it will be 
seen under the smaller visual angle A' A!, and will, 
therefore, appear smaller. 

Any cause which alters the value of the visual angle, changes 
the apparent size of the object 

294. Curved Mirrors. — Curved mirrors may be of a 
variety of forms. Those most commonly employed are 
the concave and the convex. Concave mirrors are curved 
like the inside of a watch crystal. Convex mirrors are 
curved like the outside of the crystal. 

When rays of light from illumined objects enter the eye 
after reflection from curved mirrors, the visual angle under 
which the eye views the image, is usually different from 
what it would have been, had the eye viewed the object 
directly. The apparent size of the images, therefore, is different 
from the apparent size of the objects. 

295. Concave Mirrors. — When a number of rays col- 
lect at a single point, that point is called a focus. Parallel 
rays of light falling on a concave mirror, collect after re- 



"'■,::: 




„ 










— « — *■■.-- • -^^ES f *•-•"' 


■ : ; : :V ;r: kM 


~ •■:■•••;••/ J 












':' : . $^f'''izMMMM^'. 






1 



Fig, 108.— Action of Concave Mirror on a Beam of Light. 



flection, at a point in front of the mirror called its prin- 
cipal focus. The principal focus is situated approximately 
midway between the centre of the mirror and the centre 
of the sphere of which the mirror may be conceived to 



THE REFLECTION OF LIGHT. 



193 



be a part. Thus in Fig. 108, the principal focus is shown 
at F, approximately midway between the mirror and the 
point (7, called the centre of curvature. 

If a luminous point is placed at Z, more distant from 
the mirror than its centre of curvature, the diverging rays 
which it casts on the mirror will converge, after reflection, 
to a focus at S. Conversely, if the luminous point is 
placed at £, the focus will be at L. The points L and S, 
are called respectively the longer and the shorter conjugate 
foci, because they are conjoined or mutually interchange- 
able. 

If the source of light is placed at 0, between the prin- 
cipal focus and the mirror, the rays, after reflection, will 
appear to come from a point H, back of the mirror, called 
the virtual focus. 

The conjugate foci and the principal focus are real foci, since the rays 
of light actually meet at these foci. They differ in this respect from 
virtual foci, at which the rays only seem to meet. 

296. Images Formed by Concave Mirrors. — If an 

object is placed before a concave mirror, between the 
mirror and its principal 
focus, an erect image larger 
than the object will appear 
back of the mirror. 

The manner in which the vis- 
ual image is produced by reflec- 
tion is seen in Fig. 109, where a 
person is represented as looking 
at his magnified image in a con- 
cave mirror. The rays of light 
coming from any point of the 

object as a, fall on the mirror, and being reflected from it, as shown by 
the arrow, enter the eye of the observer as though they came from a 
point a', back of the mirror ; so, also, those coming from the point b, are 
so changed in their direction by reflection as to appear to come from 
the point &'. The observer, therefore, sees an enlarged image at a' b f . 
13 R 




Fig. 109.— Virtual Image in Concave 
Mirror. 



194 



NAUURAL PHILOSOPHY. 



If the object, such as a candle, is placed before a con- 
cave mirror, at a 
shorter conjugate 
focus, an inverted 
and magnified im- 
age will be seen at 
the longer conju- 
gate focus, as shown 
in Fig. 110, at A ; 
but if the object 
is placed at the 
longer conjugate 
focus, the image 

will be inverted and smaller than the object, and will be 

seen at the shorter conjugate focus. 

The foci of convex mirrors are similar to those of concave mirrors, 
but are formed on opposite sides of the mirror to what they are formed 
in concave mirrors. 




Pig. 110.— Real Image in Concave Mirror. 







CHAPTER XVI. 

THE REFRACTION OF LIGHT. 



-»o^o 



297. Refraction of Light.— When light falls on a water 
surface, part of the light is reflected, and part of it enters 
the water. Both in the air and in the water, the light 
passes onward in straight lines. Thus, if a ray of light 
D A, Fig. Ill, falls on a 
water surface at A, it is 
reflected in the direction 
A E, just as it would have 
been from any other re- 
flecting surface. The part 
which enters the water, 
takes the straight-line 
path A G. But the direc- 
tion of the light in the 
water is not the same as 
in the air, the light being 
bent or refracted, as it enters the water. This bending or 
refraction of light always occurs when light passes from 
one transparent medium to another of different density, 
unless the light falls perpendicularly on the surface, in 
which case it enters the medium without any refraction 
or change of direction. 

195 




F G H 

Fig. 111.— Refraction of Light. 



196 



NATURAL PHILOSOPHY. 



When light is refracted, it must pass either on that side of its orig- 
inal direction, as A F, Fig. Ill, which is farther from the perpendicular 
A H, or on the side which is nearer it, as at A G. When light passes 
from a rare to a dense medium, as from air to water or glass, it is bent 
towards the perpendicular ; when it passes from a dense to a rare medium, 
as from water or glass into air, it is bent from the perpendicular.' 

298. The Index of Refraction. — The cause of refrac- 
tion is the retardation of light in dense media. The 
amount of bending or change in the direction of a ray of 
light caused by refraction, is determined by what is called 
the index of refraction, and depends on the amount of the 
retardation. 

Let D 7, Fig. 112, be a ray of light striking a water surface at 7, and 
let a circle be described with radius D 7, about the point of incidence. 
Draw the lines D N and P S, from the ends 
of the radii ID and IS, at right angles to 
NIP, the perpendicular at the point of in- 
cidence ; then the amount of the bending is 
determined by the relative lengths of the 
lines D N and S P. The ratio of D N, to 
S P, is called the index of refraction of the 
substance. Thus, if D N, is 4, and S P, is 3, 
the index of refraction will be f = 1.333. 




Fig. 112.— Kefraction of 
Light. 



299. Laws of the Refraction 
of Light. — 

(1.) The incident ray, the perpendicular at the point of in- 
cidence, and the refracted ray, all lie in the same plane. 

(2.) Between the same two media the value of the index of 
refraction remains constant, whatever may be the angle of inci- 
dence. 

(3.) The light is bent or refracted towards the perpendicular 
at the incident surface, when the ray enters a denser medium, 
and from the perpendicular when it enters a rarer medium. 

The refraction which occurs when light passes from air 
to water may be shown as follows : 



Experiment 70. — Place a coin a, in the bottom of an empty bowl 




THE REFRACTION OF LIGHT 197 

A, Fig. 113, and stand in such a position, as at c, that the coin is just in- 
visible, Observe the fact that the coin 
will become visible, when one quietly 
pours clear water into the basin. This 
is because the rays of light, which just 
graze the edge of the basin, are bent as 
they pass out of the water, and, tak- 
ing the direction b c, enter the eye of 
the observer, who sees the coin in the 
position a'. 

300. Effects Caused by ^ig. I13.-An Effect of Refraction. 

Refraction.— To an observer at c, Fig. 113, the coin a, 
appears to be raised from its true position a, to a', when 
the bowl A, is filled with water. This effect is produced 
when an observer in air looks at things in water, and is 
caused by refraction. 

In Fig. 113, the diverging pencil of light is represented 
as coming from one point of the coin ; when this light 
enters the eye, it appears to diverge from the point a' ; con- 
sequently, we see the image of this point of the coin at 
a', and not at a. Both the coin and the bottom of the 
vessel appear so raised that the water seems less deep 
tlian it really is, a circumstance which often causes errors 
of judgment as to the depth of clear water. 

A stick, partly immersed in water, appears bent where 
it enters the water, because of the refraction of the light. 

The light which comes from a distant star, situated near 
the horizon, suffers successive refractions as it enters the 
layers of air of increasing density near the earth's surface, 
so that after the star has really set, it is still visible for a 
short interval of time. 

The gradual change from daylight to darkness, called 
twilight, is another effect of the successive refractions of 
the light by the successive layers of the atmosphere. 

301. Effect of Refraction on the Apparent Posi- 
tion of Objects. — Since the position an object appears 
to occupy depends on the direction in which rays of 



198 NATURAL PHILOSOPHY. 

light coming from it enter the observer's eye, and since 
refraction alters the direction of the light, it follows that, 
usually, the effect of viewing an object through refract- 
ing media of different density, must be to change the 
direction in which it appears to be situated. 

In order that this change in the direction of the visual 
rays by refraction may occur, the eye of the observer 
must be situated in a medium of different density from 
that of the object, as, for example, when one looks at an 
object in the water, or when a medium of different den- 
sity is placed between the eye of the observer and the 
object, as in looking at an object through a heavy plate- 
glass window. 

302. Shapes of Refracting Media. — The high trans- 
parency of glass, the ease with which it may be cut or 
shaped into any desired form, and the power it has to 
bend rays of light out of their general direction, have 
caused it to be generally employed in optical instru- 
ments where a marked change in the direction of the 
visual rays is desired to be obtained by refraction. 

The change in the direction of light passing through a 
piece of glass, held between the eye of the observer and 
any object at which he may be looking, occurs both at the 
surface where the light enters the glass and where it 
leaves it. 

When the sides are parallel, as in plates of glass, the object observed 
appears to be displaced to one side of its true position. In the same 
kind of glass, the amount of this displacement increases with the thick- 
ness of the glass. 

303. Prisms. — When the glass or other refracting sub- 
stance held between the object and the observer's eye, is 
inclined, both at the face where the light enters, and at the 
face where it emerges, the substance is called a prism. Let 
the candle shown in Fig. 114, be viewed by the eye through 
the glass prism. The light from any part of the candle is 



THE REFRACTION OF LIGHT. 



199 



refracted, both on passing through the prism and on emerg- 
ing from it. The observer, therefore, sees the object con- 
siderably out of its true position. 

The amount of change 
produced in the apparent 
direction of an image by 
observing it through a 
prism, depends on the 
nature of the medium of 
which the prism is com- 
posed, on the amount of 
inclination of the faces 
where the light strikes 
and where it emerges, and 
on the angle at which the 
light strikes the prism. 

The images produced by 
prisms are necessarily indistinct, because if the pencil of diverging rays 
coming from a luminous point be large, the rays, after passing through 
the prism, fail to come to a single point or focus. This arises from the 
fact that the different rays from any luminous point will fall on different 
portions of the face, and will, therefore, have a different angle of inci- 
dence. 

304. Lenses. — In order to obtain distinct images of 
objects viewed through prism-shaped pieces of glass, it is 
necessary suitably to alter the inclination of the faces at 
the different points where the light strikes, and where it 




Fig. 114 —An Effect of Refraction. 




ABC 

Fig. 115.— Converging 
Lenses. 




D E F 

Fig. 116.— Diverging 
Lenses. 



emerges so that all the light which comes from any point 
shall collect at the same focus and enter the observer's 
eye, no matter on what part of the lens it may fall. This 



200 NATURAL PHILOSOPHY. 

is accomplished in practice by making the faces of the 
prism curved instead of straight. Such a shaped piece 
of glass is called a lens. Lenses are made in a great 
variety of forms. Those most generally employed are 
shown in Figs. 115 and 116. 

An examination of these figures will show that A, B 
and C, are thicker in the middle than at the edges ; while 
D, E and F, are thinner in the middle than at the edges. 

The first group A, B and C, are called converging lenses, 
because they cause parallel rays of light passing through 
them to converge. The second group D, E and F, are 
called diverging lenses, because they cause parallel rays of 
light passing through them to diverge. 

These lenses are named as follows : A , is a double convex lens, or more 
frequently a convex lens ; B, is a plano-convex lens ; C, is a converging con- 
cavo-convex lens, or as it is sometimes called, a meniscus ; D, is a double 
concave lens, or as it is more frequently called, a concave lens ; E, is a 
plano-concave lens ; and F, a diverging concavo-convex lens. 

305. Foci of Lenses. — When sunlight passes through 
any form of converging lens, all the rays collect at a single 
place called the focus. This is seen in the well-known ex- 
periment with a fairly large burning-glass, in which, on 
clear days, the focus at which the sensibly parallel rays of 
the sun collect is so hot that paper and wood are readily 
ignited. If the lens be held in front of the diverging 
rays from a gas-light or an electric light, the rays will also 
collect at a single point or focus, which, however, will be 
situated at a different distance from the lens than that of 
the focus of parallel rays or sunlight. The position of the 
various foci of lenses will depend on the shape of the lens, 
on the distance of the object from the lens, and on the 
kind of glass of which the lens is composed. With the 
kind of glass ordinarily employed and when the opposite 
faces of the lenses are equally curved the positions of the 
foci are given in the following paragraphs : 

306. The Principal Focus of any lens is its focus for 




THE REFRACTION OF LIGHT 201 

sunlight, or for parallel rays. Thus, in Fig. 117, the rays 
falling on the lens from its left-hand side are parallel, 
as they would sensibly be if they 
came from some object at a very 
great distance, as from the sun. 
These rays, after passing through 
the prism, meet at the point F, 
which is called the principal focus Fi * U7 £2^ F ™ ° f 
of the lens, or the focus of par- 
allel rays. In the case of a convex lens its principal 
focus is situated at about the centre of curvature of the 
face on which the light falls. Thus, in the lens shown 
in Fig. 117, the principal focus F, is situated, approxi- 
mately, at the centre of curvature of the left-hand surface. 
The principal focus of a convex lens is a real focus ; that 
is, the rays of light actually meet at this focus. 

The principal focus of a concave lens is situated near 
the centre of curvature of the face at which the light is 
incident. Thus, in the con- 
cave lens shown in Fig. 118, PL^-— -~ 

the principal focus is at F, ■ ^ ^n^si^^^ ^^—--- 

the parallel rays of light, / :i: ^^^^ 

after emerging from the ^^ 

1pti« o^Pflr to rlivpro-P sq Fig. 118 -Principal Focus of 

lens, appear to diverge, as Concave Lens. 

though they came from F. 

The principal focus of a concave lens is a virtual focus ; 
that is, the rays of light only appear to meet at this focus. 
If a source of light be placed at the principal focus of 
a convex lens, the light will pass out from the lens sen- 
sibly parallel. This is the principle of the bull's-eye lan- 
tern, in which a candle or lamp is placed in a lantern at 
the principal focus of a convex lens supported in the side 
of the lantern. Such a lantern will throw a fairly strong 
beam of light a considerable distance, because the rays, 
being parallel, are not lost by being scattered, as are those 
of an ordinary lantern. 



202 NATURAL PHILOSOPHY. 

307. Conjugate Foci. — If the luminous point, instead 
of being at a very great distance, so as to produce parallel 
rays, be brought nearer to the lens, the diverging rays fall- 
ing on the lens will, after passing through it, be brought 
to a focus at a distance further than the principal focus. 
Thus, the rays from the luminous point 0, Fig. 119, are 




Fig. 119— Conjugate Foci, 

brought to a locus at the point (7, more remote from the 
lens than its principal focus. This focus possesses the 
remarkable property that if the luminous point be placed 
at (7, its rays falling on the lens will be brought to a focus 
at C. The points C and C", are therefore called conjugate 
foci, because they are interchangeable. All conjugate foci 
are real foci. C and (?', are called respectively, the longer 
and the shorter conjugate foci. 

308. Virtual Focus. — If a luminous point be placed 

before a convex lens, 

.-^rrrTII^^ nearer to the lens than 

y**^ ^*^lfSil~ - ^ s P r i nc ip a l focus, as at 

::::::::::::: ^^^^^^ZI 0, Fig. 120, the rays, 

■r,. ,™ tt. , t, ^ after emerging from the 

Fig. 120 -Virtual Focus. , ,° °. 

lens, will diverge as 
though coming from a point K, on the same side of the 
lens as the luminous point, and at a greater distance 
from it than the distance of its principal focus. This is 
called the virtual focus. 

309. Defects or Aberrations of Lenses. — There are 
certain defects in lenses which prevent them from cor- 
rectly reproducing, in the images they form, the outlines 
and colors of the objects. These defects are called aber- 
rations. 



THE REFRACTION OF LIGHT. 203 

Lenses are subject to three aberrations : 

(1.) Longitudinal Spherical Aberration. — When the di- 
ameter of an ordinary lens is large, the portions of the 
lens near the edges have a different focus from the cen- 
tral portions ; therefore, instead of a single image being 
formed by the lens, a number of separate images are 
formed alongside of one another at different distances 
from the lens. 

(2.) Aberration of Sphericity. — When a rectilinear object 
is placed before a lens, its extremities are further from the 
lens than its central portions, and a curved image is formed 
which has its concave side towards the lens. The outlines 
of the image do not, therefore, correctly represent the out- 
lines of the object. 

(3.) Chromatic Aberration. — The rays of light which pass 
through the edges of a lens are often separated into dif- 
ferent colors just as they would be by a prism. The 
images formed by such a lens are incorrectly colored, be- 
ing bordered by prismatic or rainbow-colored fringes. 

Chromatic aberration is caused mainly by the light which passes 
through the lens, at points near its edges. It may, therefore, be par- 
tially remedied by cutting off the portions of the lens near the edges 
by the use of a diaphragm or blackened plate of metal with a central 
opening, when the light can only pass near the centre of the lens. It 
may also be remedied by certain combinations of lenses. 

Chromatic aberration is often avoided by the use of a double convex 
lens of crown glass combined with a plano-concave lens of flint glass. 
Such a combination forms what is called an achromatic lens. 

310. Combinations of Lenses. — When several lenses 
of the same type ; i. e. converging or diverging, are com- 
bined or placed so that the light passes successively 
through them, the effect is to shorten the focal length. 
This device is frequently adopted in optical instruments, 
when it is desired to obtain a lens of short focal length 
with great breadth or diameter. 




CHAPTER XVII. 

VISION AND OPTICAL INSTRUMENTS. 



=►0^0 



311. The Eye. — The human eye consists of a nearly 
spherical chamber, darkened on the inside and provided 
with two openings, one in front for the entrance of light, 
and one in the rear, for the entrance of a nerve called the 
optic nerve, which conveys the impressions of light to the 
brain, and thus enables us to see. On its entrance to the 
chamber of the eye, the optic nerve is spread out into a 
delicate net-work of nerve fibres, in what is called the 
retina, shown in Fig. 121, at K. The retina acts as a screen, 




Fig. 121.— A Section of the Human Eye, 

to receive the images formed by the lenses of the eye. At 
the opening in the front of the eye, is a transparent sub- 

204 



VISION AND OPTICAL INSTRUMENTS. 205 

stance A, called the cornea, more convex than the ball 
of the eye. Behind the cornea, and forming the colored 
part of the eye, is a circular curtain D, called the iris. A 
circular aperture C, in the middle of the iris, called the 
pupil, forms the opening through which light enters the 
eye. Immediately back of the iris is a convex lens E, 
called the crystalline lens. The space B, between the cor- 
nea and the crystalline lens is filled with a liquid called 
the aqueous humor. The large cavity L, behind the crys- 
talline lens, is filled with a clear, jelly-like substance called 
the vitreous humor. 

All these transparent portions of the eye act as a single con- 
verging lens, and form an inverted and minified image of a 
distant object on the retina. If the retinal image is sufficiently 
distinct, is properly illumined, and remains for an appreciable 
time on the retina, the object is seen distinctly. If too much 
light enters the eye through the pupil, the image is not 
seen distinctly. The iris, however, is so affected by light, 
that if too much enters the eye, the pupil contracts and 
grows smaller ; while if too little light enters, the pupil 
enlarges or dilates, and allows more light to enter the 
eye. 

Experiment 71. — Hang a small mirror immediately under a gas- 
light. Look in the mirror at the image of your eyes, and note the size 
of the pupil ; now suddenly turn the light down, leaving only sufficient 
light to see the image. The pupil will now be seen slowly to dilate. Turn 
on the gas again and the pupil will be seen to contract. 

312. Limits of Distinct Vision. Near-sightedness 
and Far-sightedness. — An object is seen distinctly, only 
when the lenses of the eye cause its image to fall directly 
on the retina. There is for every eye a certain distance at 
which it can most clearly distinguish the details of an 
object. This is called the limit of distinct vision. It varies 
with different eyes, but in normal eyes its distance is 
usually from eight to twelve inches. 

Some people have elongated eye-balls, so that the retina 

s 



206 NATURAL PHILOSOPHY. 

is farther from the cornea than in the normal eye. Such 
people are near-sighted, and can only see objects distinctly 
which are very close to the eye. The lenses of their eyes 
converge the rays so much as to cause the images of dis- 
tant objects to be formed in front of the retina. Near- 
sightedness can be remedied by the use of concave spectacles. 

Some people have flattened eye-balls, so that the retina 
is nearer the cornea than in the normal eye. Such people 
are far-sighted, and can see distinctly at comparatively 
great distances only. The lenses of their eyes cause the 
images of near objects to fall back of the retina. Far- 
sightedness can be remedied by the use of convex spectacles. 

313. Accommodation. — The extreme range of distinct 
vision extends from a few inches to an indefinitely great 
distance. Since, in order to see an object, its image must be 
focussed on the retina, it is evident that when the eye looks 
at objects at different distances, some change must occur 
which will have the effect of so altering the focal length 
of the eye as always to focus the image directly on the 
retina. This change is called accommodation. 

Accommodation is accomplished principally by a change in the con- 
vexity of the crystalline lens. This change is brought about by the 
action of certain muscles under the influence of the will. 

The eye becomes presbyopic or far-sighted with age, owing to defect 
in accommodation, that is to say, the crystalline lens remains in its 
normal condition, adjusted for distant objects, and cannot change its 
convexity. 

Fig. 1 22, represents a normal eye. In its passive condition, parallel 
rays ; i. e. rays coming from very distant objects, shown by the dotted 



Fig. 122.— Normal Eye. 

lines, are brought to a focus at the retina, which is the principal focus 
of the eye. Kays from a nearer object as at 0, would be brought to 



VISION AND OPTICAL INSTRUMENTS. 



207 



a focus at the point o, behind the retina, so that no distinct image 
would be seen with such rays. The accommodation of the eye alters 
the shape of the crystalline lens, as indicated by the dotted lines, and 
makes it more converging so as to bring the focus of the light from 0, 
on the retina. In old age this accommodation is lost and convex glasses 
have to be worn in order to focus near objects. 

Fig. 123, represents the near-sighted, elongated eye. Here, in the 
passive condition of the eye, parallel rays are brought to a focus in 




Fig. 123.— Near-sighted or Myopic Eye. 

front of the retina, while the rays from the near object 0, are then 
brought to a focus on the retina. Such an eye fails to focus distant 
objects and can only accommodate itself to objects close by. It must, 
therefore, be aided by concave glasses. 

Fig. 124, represents a flattened, far-sighted eye. Here, rays from a 
great distance, as well as from the nearer object 0, would be brought 




Fig. 124.— Far-sighted or Presbyopic Eye. 

to a focus behind the retina. Accommodation will bring the distant 
object to a focus, but not the nearer object. Such an eye cannot focus 
near objects without convex glasses. 

314. Images Formed by Lenses. — Whenever the visual 

angle under which the 

eye vieivs an image 

formed by a lens, differs 

from the visual angle 

under which the eye 

would view the object di- 

7 *' Fig, 125.— Virtual Image of Convex Lens, 

rectly, the apparent size 

of the object will differ from its real size. 




208 



NATURAL PHILOSOPHY. 



If an object be held between the principal focus of a 
convex lens, and the lens, as at A, Fig. 125, an eye placed 
on the other side of the lens will see an erect and magnified 
image of this object, apparently situated farther from the 
lens than from the object. 

If we examine any object with a magnifying-glass, we shall find, if 
we move the object towards and from the lens without taking it far- 
ther from the lens than the principal focus, that the size of the image 
will vary, but that the image will be most distinct when the object is 
held at a certain distance from the lens. It can be shown that this posi- 
tion lies very near the principal focus of the lens. The image will then ap- 
pear at the distance at which the eye sees the object most distinctly, 
that is, at its limit of distinct vision. Since the limit of distinct vision 
varies with different persons, each person must hold the glass at such a 
distance from the object that the image formed shall be at his limit of 
distinct vision ; that is, he must focus the glass to suit his eyes. 

315. Images at Conjugate Foci. — If an object be 
placed before a convex lens, at a shorter conjugate focus, 
an enlarged and inverted image will be formed at its longer 
conjugate focus; but if the object be placed at the longer 

conjugate focus, an 
inverted and mini- 
fied image will be 
formed at the short- 
er conjugate focus. 
In Fig. 126, the ob- 
ject A J5, is placed 
at the longer conju- 
gate focus of the 

Fig, 126.— Inverted Image at Conjugate Focns. i * s\ j 

6 s j s convex lens 0, and 

an inverted image, smaller than the object, is seen at A B\ 
As this image is real, it may be received on a screen as 
shown. 

All images formed by convex lenses at their conjugate foci are real 
and are inverted. Those formed at the longer conjugate foci are magni- 
fied and those formed at the shorter conjugate foci are minified. 

316. Optical Instruments are any combination of 
lenses, or of lenses and mirrors, that enable us to exam- 




VISION AND OPTICAL INSTRUMENTS. 



209 



ine the images of distant or of near objects. Nearly all 
optical instruments employ more than a single lens, yet, 
so far as the production of the image is concerned, many 
of them act as though a single lens only was present ; for 
example, the simple microscope, the photographing camera, 
the magic lantern, and the camera obscura, are optical in- 
struments in which practically but a single lens is em- 
ployed. 

317. The Simple Microscope employs a single lens 
or combination of lenses, A, Fig. 127. 
The object to be examined is placed on 
a stage C, at a distance from the lens 
A, rather less than its principal focus. 
An eye placed above A, sees an en- 
larged and erect image of the object. 
A screw V, is used for focussing. The 
mirror M, throws light on C. 

318. The Photographing Camera. 

—The photographing camera, Fig. 128, Fig. 127.-The Simple 
consists of a lens placed in a tube at Microscope, 

A, inserted in the camera box G. The image of an 
object, for instance, a person placed in front of a tube A, 
at the longer conjugate 
focus, is received on a 
screen of ground glass 
E, as an inverted and 
diminished image. This 
image is sharply fo- 
cussed on the screen by 
means of the screw D. 
The screen is then re- 
moved and replaced by 
a plate covered on one 
face with chemicals sensitive to light. The image now 
falls on the sensitive plate, and is impressed upon it by 

14 





Fig. 128.— The Photographic Camera, 



210 



NATURAL PHILOSOPHY. 



the light causing certain changes in the chemicals cover- 
ing its surface. 

319. The Magic-Lantern. — In the magic-lantern, Fig. 
129, a partially transparent picture A, is placed in an in- 
verted position, before a lens i?, 
at its shorter conjugate focus 
and is received as an enlarged 
and erect image on a screen 
placed in front of the lantern. 
For the purpose of strongly 
illumining the picture, a mir- 
ror is placed at M, behind the 

Fig. 129.-The Magic Lantern, gQurce rf ^ ^ and ^ ^ 

(7, called the condenser, is placed in front of the light, 
and between it and the picture. 

320. The Camera Obscura is an arrangement by 
which a distinct image of an object can be thrown on a 





Fig. 130.— Camera Obscnra. 



sheet of paper for convenience in sketching. A mirror 
IT, Fig. 130, is placed in an inclined position above the 



VISION AND OPTICAL INSTRUMENTS. 



211 



lens L. The light from a distant object is reflected from 
the mirror to the lens, which forms an image of the object 
on a sheet of paper placed on a table B y at a suitable dis- 
tance below. 

Experiment 72. — Place a small convex spectacle lens in a suitable 
hole in the top of a box ; support a piece of looking-glass directly over 
the lens, and inclined at an angle of 45°. Observe that on holding a 
sheet of paper inside the box, at the proper distance from the lens, the 
side of the box having been removed for that purpose, an image of any 
object in front of the mirror will be seen on the paper. 

321. The Compound Microscope employs at least two 
lenses or sets of lenses, as shown in Fig. 131. Instead of 
looking directly at the 
object, the magnified 
image formed by one 
set of lenses is viewed 
through a second lens, 
which still further 
magnifies it. The lens 
which is placed nearer Fi * 13L " Tlie Com P oimd Microscope - 
the object, is called the object-lens or object-glass ; the lens 
nearer the eye is called the eye-lens. The object b a, is 
placed before the object-glass 0, at a shorter conjugate focus, 
and an inverted and enlarged image formed by it at a f b'. 
The image a' b\ lies nearer to the eye lens (7, than its 
principal focus. The eye at D, therefore, sees an erect 
and greatly enlarged image at A B. 

322. The Telescope, like the microscope, employs two 
lenses or sets of lenses : the lens nearer the object is called 
the object-lens, and that nearer the eye is called the eye-lens. 
Telescopes may be constructed either with both object-lens 
and eye-lens of glass, when they are called refracting tele- 
scopes; or a concave mirror may be used in the place of 
the object-lens, when they are called reflecting teleseopes. 

In the refracting telescope shown in Fig. 132, 0, is the 
object-glass and E, the eye-lens. 




212 



NATURAL PHILOSOPHY. 



Since the telescope is used for viewing distant objects, 

the object is necessarily situated at a longer conjugate focus. 

Its image, therefore, seen at a 6, is inverted and diminished. 

A 

DM 




Pig, 132 —The Refracting Telescope, 

As in the microscope, this image falls within the principal 

focus of the eye-lens, and is, therefore, viewed by the eye 

placed at Z>, as a magnified image A B. 
323. Reflecting Telescopes employ a mirror for the 

object-glass instead of a lens. In Fig. 133, we have a 

representation o f 
Herschel's reflect- 
ing telescope, i n 
which the mirror 
if, forms an image 
a 6, of a distant ob- 
ject, which, viewed 
by the eye at 




Fig. 133 —The Reflecting Telescope. 

through the eye-lens E, appears as a magnified image at 
a'V. 



The telescope owes its great penetrating power to the great size of the 
object-glass. The amount of light which can enter the unaided eye from 
a distant object, is limited by the size of the pupil ; but by the use of a 
telescope, all the light which falls on the object-glass is swept into the 
eye. The penetrating power of the telescope will, therefore, be as much 
greater than that of the eye, as the area of the object-glass is greater 
than the area of the pupil of the eye. In a large reflecting telescope 
made by Kosse, the area of the concave mirror which acted as the ob- 
ject-glass, was 518,400 times greater than the pupil of the eye. This 
instrument collected, even after allowing that half the light was lost by 
reflection, rather more than 250,000 times as much light as the unas- 
sisted eye. 



VISION AND OPTICAL INSTRUMENTS. 213 

324. Binocular Vision. — When we look at an object, 
an image is produced on the retina of each eye. Under 
normal conditions these images produce the sensation of a 
single picture only. The image formed by the right eye is 
not identical with that formed by the left eye, but contains 
more of the right side of the object, while the image of 
the left eye contains more of the left side. The effect of 
combining both these images in a single picture is to give 
an appearance of solidity to the object. Vision obtained 
in this way by two eyes is called binocular vision. Besides 
producing the appearance of solidity, binocular vision 
aid us in forming an estimate of the relative distance of 
objects. 

Experiment 73. — Hold a finger of one hand in front of the face, 
and about six inches away, at the same time focussing the eyes on a dis- 
tant object. The finger will appear double. Now look at the finger and 
the distant object will appear double. 

325. Stereoscope. — The stereoscope is a device for 
readily merging the images of two separate pictures into 
a single image, and so obtaining an appearance of solidity 
and perspective. The two pictures are taken from two 
slightly different points of view. 




CHAPTER XVIII. 

CHROMATICS. 

«K>>^CK> 



326. Dispersion of Light. — The Spectrum. — Just as 
the so-called simple notes of musical instruments seldom 
consist of a single tone, being accompanied by a number of 
additional or over tones, so sunlight, though apparently of 
one color, contains light of many different colors. If sun- 
light coming in the direction FK, through a narrow slit F, 
in the shutter of an otherwise darkened room, be allowed to 
pass through a prism P, as shown in Fig. 134, the light 

will not only be bent 
out of its course by 
refraction, but it will 
also be separated into a 
number of differently 
colored rays, which, if 
allowed to fall on a 
screen, will be spread 
out in the form of a 
brightly colored band 
Fi?, called a spectrum. 

There is almost an infinite variety of colors in the spectrum of sun- 
light ; but, for the sake of simplicity, we may distinguish seven well- 
marked regions of color, which are called violet, indigo, blue, green, 
214 




Pig. 134,— Formation of a Spectrum by a 
Prism. 



CHROMATICS. 215 

yellow, orange and red. The order of these colors may be easily re- 
membered by the word vibgyor, which is formed by putting together the 
first letters of the names of the colors. 

The different colors of the spectrum are refracted in 
different degrees; thus, an inspection of Fig. 134, will 
show that the red is the least, and the violet the most, 
turned out of its course ; in other words, the different 
colors of the spectrum differ in their refrangibility, red 
being the least refrangible, and violet the most refrangible. 

The separation of light into different colors, in this way, 
by its passage through a prism, is called dispersion. 

The differences in color are due to the same causes as are the differences 
of tone or pitch of sound-waves ; viz., to the difference in the frequen- 
cies, or the number of vibrations per second. The reds and oranges cor- 
respond to the grave tones, and the blues and violets to the shrill tones. 

The range of sensibility of the eye to color is far less than that of the 
ear to sound, the eye being sensitive to rather less than one octave, 
while the ear is sensitive to about eleven octaves. 

327. The Re-combination of the Colors of the 
Spectrum. — When all the colors of the solar spectrum 
act at the same time on the eye, they produce the sensa- 
tion of w T hite light like that of the sun. This may be 
shown by causing the spectrum to 
fall on a convex lens, and allowing 
the light so collected, to fall on a 
screen placed at the focus of the lens. 
The spot of light formed on this 
screen will be no longer colored, but 
will be pure white. 

Experiment 74.— Cut out a disc of white -£ig, 135 —Color Disc, 

cardboard, and paint on it, in spaces corre- 
sponding to those as shown in Fig. 135, seven colors, as near as can be 
obtained to those seen in the solar spectrum or the rainbow. Stick a 
pin through the centre of the disc, and whirl it rapidly around with 
the fingers, observing that, when it is turning fast enough, it will ap- 
pear to be colored grayish white, from the mingling of the different 
colors. 




216 NATURAL PHILOSOPHY. 

328. Cause of the Dispersion of Light.— All waves 
of light, no matter what their frequencies, are believed to 
pass through free ether with the same velocity. Thus all 
colors of light emitted from the sun are believed to reach 
the earth in the same interval of time. 

When the complex wave of white light enters the dense substance of 
a prism, the different wave lengths, or the different colors of light, 
are differently refracted, and therefore take separate paths ; or, in other 
words, the white light undergoes dispersion. 

Although different-colored lights move with the same velocity through 
the free ether, yet they move through the ether which occupies the 
space between the molecules of solids with different velocities. Each 
transparent solid has its own rate of transmission of light rays, and in 
the same substance this rate varies with the frequency. 

329. The Cause of Color.— When sunlight falls on 
any colored body, as, on a piece of red cloth, nearly all 
the colors of the light but the reds are absorbed, and these 
only being given off, the cloth appears red ; so in a green 
leaf, all the colors but the greens are absorbed, and the 
greens only are given off. The colors of bodies are there- 
fore, due to the light which falls on them. In the dark no 
body has color. 

If a body of any color, such as pure red, be illumined 
by light which contains no red, the body will appear 
black. Thus, if a piece of bright red flannel be held in 
the pure green light of the solar spectrum, it will appear 
black. 

Experiment 75.— Eoll a piece of lamp-wick into a loose ball, and 
soak it for a few moments in a strong solution of table salt in water. Then 
place the wick in a saucer, pour some alcohol over it, and set fire to it. 
It will burn with a pure yellow light. Examine different colored objects, 
such as zephyrs, cloths, or silks, by means of this light, and observe that in 
an otherwise darkened room, they will appear to have lost their colors, 
except those which are yellow. Now bring a lighted candle near any of 
the objects, and, since the lighted candle gives off light of all colors, the 
color of the fabrics will again appear. 

330. Complementary Colors. — When all the colors 



CHROMATICS. 217 

of the spectrum are combined, white light is produced, 
but if one of the colors be removed the mixture will no 
longer produce white. Thus, if the red is removed from 
the spectrum, the admixture of the remaining colors will 
produce a certain shade of green. This green, if mixed 
with the red that was removed will produce white light. 
Such a green is said to be the complementary color to the 
red, since it is what such red requires to complement or 
fill it to its full measure of white. 

The following colors are complementary to each other ; 

Eed Green. 

Violet Yellow. 

Blue Orange. 

331. The Rainbow. — When sunlight passes through 
falling rain-drops, it is separated into its different colors, 
each rain-drop acting as a prism. On entering the drops, 
the light is reflected from the surfaces farthest from the 
sun, and passes out separated into its prismatic colors, 
having undergone refraction in passing through the drop. 
This light entering the eye of an observer, standing with 
his back to the sun, causes him to see a band of colors 
called the rainbow. Rainbows are largest when the sun is 
near the horizon, as when nearly setting or shortly after 
rising. 

332. Fraunhofer's Dark Lines.— When the spectrum of a narrow 
slice of sunlight is examined, it is found to be discontinuous, numerous 
dark lines crossing it. These dark lines indicate places where certain 
frequencies of light are absent. 

The dark lines of the solar spectrum were discovered by Wollaston, 
in 1802. He failed, however, to recognize their importance. They 
were subsequently re-discovered by Fraunhofer, who pointed out their 
significance and mapped out the positions of several thousands of them. 
They are, therefore, known as Fraunhofer' s lines. The Fraunhofer lines 
are conveniently located in the spectrum by reference to eight promi- 
nent lines, named A, B, C, D, E, F, G and H. 

T 



218 



NATURAL PHILOSOPHY. 



The positions of these lines may be seen in the table given below, 1 
also the frequencies and wave lengths, in hundred-mil lionths of a cen- 
timetre. 

333. Spectrum Analysis is based on the fact that the 
light given off by any gaseous or vaporous substance, 
heated to luminosity, is characteristic of that substance, 
that is to say, no two luminous gaseous or vaporous sub- 
stances give off exactly the same kind of light. In order 
to determine the composition of a substance, it is, there- 
fore, only necessary to reduce the substance to a gas or 
vapor, heat the gas or vapor until it emits light, and then 
examine that light. 

But the unaided eye would not be able to detect all the 
differences in the light given off by different glowing gases 
or vapors, unless the different colors of such light were 
separated from one another by its passage through a 
prism. This is accomplished by the use of an instru- 
ment called the spectroscope. 

334. The Spectroscope consists of the following parts : 
(1.) Any suitable means for volatilizing the substance to 

be examined and heating its vapor to luminosity. 

(2.) A narrow slot in a plate so as to limit the amount 
of light which enters the spectroscope to a narrow slice. 



Names. 



red 



Line A 
Centre of 

Line B 

Line C 

Centre of orange . . . 
Line D (middle of pair) 
Centre of yellow . . . 
Centre of green .... 

Line E 

Line F 

Centre of blue .... 

Line G 

Line H 



Frequencies per 
second. 



394,500,000,000,000 



436,900,000,000,000 
457,200,000,000,000 



509,200,000,000,000 



569,300,000,000,000 
617,900,000,000,000 



696,500,000,000,000 
762,800,000,000,000 



Wave-lengths 

in microns or 

millionths of 

a metre. 



0.7604 
0.7000 
0.6867 
0.6562 
0.5972 
0.5892 
0.5808 
0.5271 
0.5269 
0.4861 
0.4732 
0.4307 
0.3933 



CHROMATICS. 



219 



(3.) A prism, or a number of prisms, through which the 
slice of light passes for the formation of a spectrum. 

(4.) A telescope with which to examine the spectrum 
so formed. 

A form of spectroscope is shown in Fig. 136. The substance is vola- 
tilized by the flame of a Bunsen burner G. For metals or other refrac- 




Fig. 136,— The Spectroscope. 

tory bodies, a stream of electric sparks is used. The narrow slot is 
placed in the tube 2?, furnished with lenses so as to cause the rays pass- 
ing through the slot to fall on the prism P, parallel to one another. The 
telescope A , is used for the purpose of examining the spectrum. The 
telescope C, is provided for the purpose of measuring the relative dis- 
tances of the lines of the spectrum. 

335. Solar Spectroscopic Analysis is based on the 
presence of the Fraunhofer dark lines. 

A luminous gas or vapor is opaque to light of the same frequency as 
that it is itself emitting. This fact is known as Stokes's law. 

Burning sodium, for example, emits a characteristic yellow light, which 
will permit all the colors of light of a continuous spectrum, except its 
own, to pass through it. If, therefore, the light from an incandescent 
solid be passed through the flame of a Bunsen burner, in which sodium 
is burning, its spectrum will show the absence of the particular color 
of yellow the sodium vapor itself emits ; or, in other words, a dark line 
will appear at this part of the spectrum. 

The portion of the spectrum where this line occurs is not absolutely 



220 NATURAL PHILOSOPHY. 

devoid of light, since the yellow light from the faintly luminous flame 
is present ; but, by contrast with the brighter light of the incandescent 
solid, it appears dark. 

336. Cause of the Fraunhofer's Dark Lines. — The Fraunhofer 
lines are absorption lines. The central body of the sun gives a continu- 
ous spectrum, but while the light is passing through the masses of 
glowing gases and vapors which surround the body of the sun, a selec- 
tive absorption occurs, and that light which is of the same color as the 
light these gases emit, is stopped or absorbed, and thus the dark lines 
are formed. 

The spectroscope shows the portions of the spectrum in which these 
dark lines occur, and from this we infer the presence of such substances 
in the sun' s atmosphere as would, when heated, emit light of the same 
color as that belonging to the parts of the spectrum where the dark lines 
are observed. 

337. Interference of Light. — The beautiful colors 
seen in soap bubbles, or in films of oil floating on water, 
are due to what is called the interference of light. We 
have already seen that when two separate sources of 
sound simultaneously affect the same particles of air, they 
may either augment or diminish each other's intensity, 
and that under certain conditions, one may entirely annul 
the action of the other. The same is true with light. 
In the case of a soap-bubble, or a thin film of oil, the 
light directly reflected from the surface of the film in- 
terferes with the light which is reflected from its lower 
surface. In certain portions of the film some of the 
colors in these rays completely obliterate one another, 
thus leaving the remainder of the light visible as rain- 
bow tints. Similar effects of interference are seen in 
mother of pearl, and in the wing-cases of certain beetles. 

338. Diffraction. — The water behind a large post, that projects 
above a water surface, is not entirely shaded from small waves moving 
over the surface. A part of the energy in the wave is expended in pro- 
ducing what may be called secondary waves, which move in all directions 
from the post and thus partly disturb the water on the farther side. The 
same is true of light. When waves of light graze the sharp edge of 
a body, secondary waves are formed at the edge, which pass into the 



CHROMATICS. 



221 



position of the shadow of the body. This phenomenon is called diffrac- 
tion, Under certain circumstances these secondary light-waves may in- 
terfere with each other and thus produce prismatic colors, similar to 
those seen in the thin films. 

339. Double Refraction. — Some media, such as certain varieties 
of calc spar, possess the curious property of splitting up the rays of 
light that pass through them in certain directions into two separate 
rays, so that any object seen through them in certain directions, such as 
the dark circle shown in Fig. 137, appears double. This effect is called 




Fig, 137 —Double Refraction. 

double refraction, and is due to the fact that the substance possesses a dif- 
ferent velocity of transmission of light in different directions. 

340. Irradiation. — A white object, or an intensely illu- 
mined object of any color, when seen on a dark ground, 
appears to be larger than it really is. Thus, the white 
circle on a black ground, Fig. 138, appears to be larger 
than the black circle 
on the white ground, 
though they are actu- 
ally the same size, as 
may be proved by 
measurement. This ef- 
fect is known as irra- 
diation, and is due to 
the impression produced on the retina gradually extend- 
ing beyond the outlines of the image. Irradiation varies 
with different people, and with the time at which the 
object is viewed. 




Fig, 138.— Irradiation. 



222 NATURAL PHILOSOPHY. 

The moon, from the effects of irradiation, appears larger 
at the horizon than when directly overhead. 

341. Effects Produced by Contrast of Colors.— If 

we look for some time at a bright-red object on a black 
ground, such as a red wafer on a sheet of black paper, 
and then look at a sheet of white paper, we shall see a 
green image of the wafer. If we similarly look at a 
blue wafer, we shall see an orange image on the white 
paper. These images are called accidental images. Their 
cause is but imperfectly understood. Accidental images 
of colored objects are always of the same outline as the 
object, and of the complementary colors. 

These images are formed when different colors are placed side by side, 
and cause each color to appear as if mixed with the complement of the 
color beside which it is placed. Thus, red placed beside yellow, causes 
the yellow to appear as if mixed with the complement of the red or 
green ; while the yellow causes the red to appear as if mixed with 
violet, the complement of the yellow. 

Complementary colors enhance each other by contrast, thus red and 
green, appear respectively redder and greener by the effects of con- 
trast. 

342. Actinism. — By actinism is meant the chemical 
effects of light. 

Light possesses the power of causing various chemical 
decompositions. Photography is based on this fact. Sil- 
ver chloride blackens on exposure to sunlight. The sun- 
light falling on the leaves of plants causes the decompo- 
sition of the carbonic acid gas which the leaves absorb 
from the atmosphere; the plant retaining the carbon, for 
the formation of its woody tissues, and throwing off the 
oxygen. The fading of carpets and tapestry is caused by 
the actinic power of light on their coloring matters. 

A strip of paper, freshly washed in a solution of qui- 
nine sulphate, gives off a fluorescent light, that is, becomes 
momentarily self-luminous, when placed in different parts 
of a spectrum formed by a prism of quartz, which is trans- 



CHROMATICS. 223 

parent to the actinic rays. This effect is found to be least 
in the red, and greatest in the violet, but extends far be- 
yond the violet, thus showing the existence of an invisible 
spectrum of ultra-violet rays. 

343. The X-Rays or the Rontgen Rays. — A new 
species of radiation, the exact nature of which is not yet 
understood, has been recently discovered by Prof. Rontgen, 
of Bavaria, for which he has proposed the name of the X- 
rays (i. e. unknown rays). These rays are produced by 
sending electric discharges through exhausted glass tubes. 

The X-rays, or, as they are frequently called, the Ront- 
gen rays, possess the curious property of readily passing 
through many substances opaque to light, and afterwards 
producing photographic images on suitably prepared plates 
on which they strike. By these means it is possible to 
obtain photographs of the bones of the body, while sur- 
rounded by the flesh. 

Fig. 139, is a photograph obtained by this means of the 
bones of a living hand. To take this picture, the hand 
was placed over a sensitive photographic plate, which was 
wrapped in black cloth to prevent the action of ordinary 
light. 

The discharge of a Ruhmkorff coil, passed through an 
exhausted tube, produced X-rays. The X-rays falling 
on the hand readily penetrated the flesh and the black 
cloth and acted on the photographic plate placed beneath. 
The bones of the hand, however, were opaque to the rays, 
so that where the plate was so protected, no action was 
effected. On developing the plate, a shadow picture of the 
bones of the hand was obtained. Such a picture is called 
a radiograph or X-ray picture. 




FIG. 139-RADIOGRAPH OF HAND, 




PART IV. 
Heat and Electricity. 



-*0>©<0 



CHAPTER XIX. 



THE NATURE OF HEAT. 



344. The Cause of Heat. — The molecules of all kinds 
of matter are never in a condition of rest, but are con- 
tinually in rapid to-and-fro motions or vibrations towards 
and from one another. The hotter the body, the more ener- 
getic are these molecular vibrations. If matter were abso- 
lutely devoid of heat, these vibrations would be entirely 
absent. This condition, probably, never occurs. 

As the temperature of a body increases, both the speed with which 
the molecules move, and the rate at which they vibrate increase ; or, in 
other words, both their energy of motion and their frequency increase. 
If the temperature be raised sufficiently high, the body will glow and 
emit a red light. As the temperature increases, orange and yellow light 
accompany the red ; and, at still higher temperatures, the other colors 
of the spectrum appear, and the substance becomes white hot. 

The vibrating molecules of a heated body impart a wave 
motion to the surrounding ether, producing what is known 
as radiant light and heat. Radiant heat differs in no re- 
spect from light, save in the frequency of the vibrations. 
Ether waves, of frequencies between 392,000,000,000,000 
and 757,000,000,000,000, produce on the eye the sensation 
of light. Ether waves of all frequencies produce the ef- 

15 225 



226 NATURAL PHILOSOPHY. 

feet of heat, but higher or lower frequencies produce the 
effect of heat without light. 

345. Heat as a Form of Energy. — In all cases a body 
becomes hot when the energy of the to-and-fro motions 
of its molecules is increased. This may be done : 

(1.) By placing it in contact with a hot body. 

(2.) By causing it to combine chemically with some 
other body, as by setting it on fire. 

(3 ? ) By allowing it to absorb radiant heat. 

In all these cases the energy of motion of the molecules 
increases. Heat, therefore, is a form of energy, and like 
all energy may be measured in foot-pounds. A given 
weight of a substance, heated to a given temperature, 
possesses a greater amount of energy than if heated to a 
lower temperature. In other w r ords, when bodies absorb 
heat, they acquire a greater store of energy ; when they 
lose heat, they part with some of their energy. Heat 
energy is, therefore, a form of molecular energy. All 
bodies possess some heat energy. 

Heat was formerly believed to be an imponderable fluid called caloric. 
According to this view a body became heated when it absorbed or took 
in caloric, and grew cold when it threw it out. This view is now en- 
tirely abandoned. Heat is now known to be molecular motion. 

Heat energy is capable of existing in two distinct forms : 

(1.) As energy of motion in the molecules of ordinary 
matter. 

(2.) As energy of wave motion in the universal ether. 

In the sun, heat energy is the energy of moving mole- 
cules. The heat energy of the sun is transmitted to the 
earth as radiant energy ; i. e. energy of wave motion in the 
ether. On reaching the earth this energy is absorbed and 
becomes the energy of moving molecules. 

346. General Effect of Heat. — Although we cannot 
see the molecules vibrating in a body, yet we can see the 
effect which these vibrations produce. The hotter the 



THE NATURE OF HEAT 227 

body, the more energetic will be the motion of its mole- 
cules, and the greater will be the distance through which 
they move. In this way the force of molecular attraction is 
partially overcome, and the body expands. When a body 
loses heat, its molecular motion becomes less ; attraction 
again draws the molecules together, and the body contracts. 

During their to and-fro motions, the molecules of a heated body move 
in sensibly straight lines until they strike or collide against one another. 
When it is remembered that the frequencies of the molecular heat vibra- 
tions are counted in trillions per second, it will be seen that the re- 
peated shocks or collisions must have the effect of weakening the 
cohesive attraction of the molecules. The body, therefore, expands. 
As the temperature increases, the more rapid motion of the molecules 
causes the collisions to become more frequent and severe, so that the 
amount of expansion increases. 

347. Temperature. — When two bodies are placed in 
contact, each gives some of its heat to the other. If they 
are equally hot, each will give the other as much heat as 
it receives, and it will appear as if no heat passed between 
them. When no heat appears to pass between two bodies 
that are placed in contact, they are said to be at the same 
temperature. If, however, one of the bodies is hotter than 
the other, it gives more heat than it receives and, there- 
fore, may be said to be at a different temperature. 

The temperature of a body is measured by an instru- 
ment, called a thermometer. 

348. Thermometers depend for their operation on the 
expansion of a liquid contained in a glass tube. Mercury 
is usually employed for this purpose, though alcohol is 
sometimes used. 

A thermometer consists of a long, straight tube A B, 
Fig. 140, of small internal diameter, closed at the upper 
end, and widened at the lower end into a bulb C, prefer- 
ably cylindrical in shape. The bulb C, and part of the 
tube, contain mercury ; the space above the mercury in 
the tube is exhausted, so as to produce a vacuum. When 



228 N A TUBAL PHILOSOPHY. 

the thermometer is taken into a hot place, the mercury 
becoming warmer, expands and rises in the tube ; when 
taken into a cold place, the mercury losing heat, con- 
tracts, and falls in the tube. The tube is graduated or 
marked off into equal spaces, called degrees. 

349. Construction of a Thermometer. — Before the 
thermometer tube is closed at the top, the bulb and part 
of the tube are filled with cold mercury. The bulb is 
then carefully heated. As the mercury grows hotter, it 
expands, and, filling the tube, drives out all the air, and 
begins to flow over the top. The bulb is now taken away 
from the source of heat, and at the same time the upper 
end is completely closed, by being melted in the flame of 
a blow-pipe. As the bulb cools, the mercury falls in the 
tube, leaving a vacuum or empty space above it. 

The next step is the graduation of the tube, or its divi- 
sion into degrees. For this purpose, the bulb is first 
dipped into melting ice, and a mark made at the point on 
the tube to which the mercury sinks. The bulb is then 
exposed to the vapor rising from boiling water, and an- 
other mark made at the point to which the mercury rises. 
These two points are called respectively the freezing point 
and the boiling point The length of the tube between the 
freezing and boiling points is then divided into a certain 
number of equal parts, called degrees, and the remainder 
of the tube, that is, the part below the freezing point and 
above the boiling point, is similarly graduated, or divided 
into degrees of the same length. 

There are two thermometric scales in common use : the 
Fahrenheit and the Centigrade. These two scales are rep- 
resented in Figs. 140 and 141. In the Fahrenheit scale, 
Fig. 140, that length of the tube which lies between the 
freezing and boiling points is divided into 180 equal parts 
or degrees. The freezing point is marked 32°, and the 
boiling point 212°. 






THE NATURE OF HEAT 



229 



212° 



32° 



100° 



0° 







Fig. 140. 
Fahrenheit, 



In the Centigrade scale, Fig. 141, the distance between 
the freezing and boiling points is divided into 100 equal 
parts. In this scale the freezing point 
of water is marked 0°, or zero, and the 
boiling point 100°. Degrees of the 
Fahrenheit scale are indicated by an 
F., or Fahr. ; those of the Centigrade 
scale by a C. Thus, the freezing point 
of water is 32° F., or 0° C. 

The zero of the Fahrenheit and the Centi- 
grade scales is arbitrary. Absolute zero would, 
of course, be found when molecular motion 
absolutely ceases. Considerations based on 
the expansion and contraction of gases, and 
on other physical phenomena, estimate the 
absolute or natural zero of the thermometric 
scale at -273° Centigrade or -459° Fahren- 
heit. In the scale of absolute temperature, 
therefore, —273° below the zero of Centigrade 
scale is taken as the absolute zero. Absolute 
temperature may be obtained by adding 273° 
to the indications of a Centigrade thermometer, or 491° to those of a 
Fahrenheit thermometer; thus water boils at 100° C, or 373° absolute 
temperature, or at 212° F. or 704° absolute temperature. 

350. Uses of Thermometers. — We cannot rely on our 
sensations to determine accurately the difference between 
the temperature of two bodies. If the hand, while warm, 
is plunged into a basin of tepid water, the water will feel 
cool ; but if the hand is cold, when plunged into the same 
tepid water, the water will feel warm. Again, if in winter 
we come from the cold outside air into an entry or hall, 
the entry or hall feels warm ; but if we go into the entry 
from the warmer parlor, then the entry feels cold. In a 
room where there is no fire, and all the objects are at the 
same temperature, a marble mantel feels cold to the hand, 
while a hearthrug feels warm. The indications of a ther- 
mometer are not open to these objections. 

u 



Fig, 141. 
Centigrade. 



230 NATURAL PHILOSOPHY. 

It is evident that hot and cold are only relative terms, 
since the same body may be hot when compared with one 
body, and cold when compared with another. 

351. Expansion of Solids. — The general effect pro- 
duced in all kinds of matter by an increase of tempera- 
ture is to cause it to expand, while a decrease of tempera- 
ture causes it to contract. Solids expand less than liquids, 
and liquids expand less than gases. Different solids ex- 
pand differently in amount when heated one degree. Zinc, 
lead, and tin are among the most expansible of the metals, 
and steel and platinum among the least expansible. Ice is 
more expansible than zinc. Most crystalline solids ex- 
pand more in one direction than in another ; while most 
bodies that are not crystallized, expand equally in all 
directions. 

352. Examples of the Expansion of Solids. — When 
solid bodies expand or contract, they exert considerable 
force. The tires of wheels are made of such a size that, 
when cold, they will not go on the wheel; so they are 
heated until they are large enough to slip on easily, and 
when cold they contract and fit very tightly to the wheel, 
holding its parts firmly together. 

The rails of railways are laid with some little space be- 
tween the ends, so as to leave room for expansion. 

The snapping and crackling of a stove, when suddenly 
heated by building a fire, or when suddenly cooled by 
opening the stove door, is caused by the unequal expan- 
sion of the metal at different parts. 

Experiment 76. — A glass vessel may readily be cut into any desired 
shape as follows : Suppose it is desired to cut off the top of a broken 
bottle. Start a crack at the edge of the bottle by heating and suddenly 
cooling it. From the end of this crack, draw a chalk line in the direc- 
tion in which it is desired to cut the bottle. Heat the end of a poker red 
hot and hold the heated point firmly against an uncracked portion of 
the glass, on the chalked line, and a little distance beyond the crack. In a 
moment a faint click will be heard, and the crack will extend to the 



THE NATURE OF HEAT. 231 

point where the poker touches the glass. Lift the poker from this point, 
and place it again on the chalked line a little beyond the crack, and so 
on until the crack has extended all around. 

The table below gives the expansion of a number of 
different solid substances. 1 The expansion per degree is 
very nearly the same at all temperatures between the tem- 
perature of the melting point of ice and the boiling point 
of water. 

This table is used as follows : A copper trolley wire, at the tempera- 
ture of melting ice, is 100 feet in length : what will be its length at the 
temperature of boiling water? Here 100° - 0° = 100°, and 100° x 
0.000017 = 0.0017 feet expansion per foot, so that 100 feet will expand 
100 x 0.0017 = 0.17 feet = 2.04 inches. 

Thick glassware is sometimes broken, when suddenly 
heated or cooled, on account of unequal expansion or 
contraction. When hot water is poured into a thick 
glass tumbler, the inside of the glass expanding before 
the outside becomes warm, may cause the tumbler to 
break. 

353. Expansion of Liquids. — Liquids expand when 
heated and contract when cooled, proportionately more 
than do solids. 

Water presents some curious phenomena in its expan- 
sion and contraction. When at the temperature of melt- 
ing ice, or 32° Fahr., water, if heated, contracts and grows 
denser, and this continues until the temperature of 39.2 

1 Linear Expansion for 1° C. 

Ice 0.000050 of its length. 

Zinc 0.000030 " 

Lead . . . " 0.000028 " " 

Tin 0.000020 " " 

Silver 0.000019 " " 

Copper 0.000017 " 

Gold 0.000015 " " 

Iron 0.000012 " " 

Steel 0.000011 " " 

Platinum 0.000009 " " 



232 



NATURAL PHILOSOPHY. 




Fig. 142.— Expansion of 
Water by Cold. 




Fig. 143 —Effect of Maximum 
Density on Freezing. 



1 Alcohol 1.11 

Linseed oil . . . * . . 1.08 
Turpentine 1.07 



Sulphuric acid .... 1.06 

Water 1.0466 

Mercury 1,015 



Fahr. is reached ; when heated above this point, however, 
it expands like most other sub- 
stances. The temperature of 39.2° 
Fahr. is called the temperature of 
the maximum or greatest density of |^ 

water. When water is at the tern- 1 

perature of its maximum density, 
it will expand, whether it be heated 
or cooled. 



Experiment 77. — Fit a narrow glass 
tube A, Fig. 142, tightly in a cork B, and in- 
serting the cork into the neck of a large bot- 
tle C, fill the bottle and tube with water to 
the point A. Place the bottle in a pan D, 
and surround it with layers of broken ice 
and salt. As the water is cooled, the column 



of water in the tube will fall, thus proving that the water is contract- 
ing. But when the water is cooled to 39.2° Fahr., the column will cease 
falling, and will begin to rise, although the water is still growing colder. 

The table below gives the expansion of different liquids 
at the temperature of 212° F. ; the volume at 32° F. being 
unity. 1 It will be seen from this table that of all the liquids 
named, mercury expands the least, and alcohol the most. 
354. Peculiarities of the Freezing of Large Bodies 
of Water. — Let A, Fig. 143, be a deep lake of fresh water, 

in which the water is at the 
temperature of, say, 50° F. If 
the air grows cold, the water 
at the surface of the lake grows 
cold and sinks, because it con- 
tracts and becomes heavier 
than the rest of the water. When all the water in the 
lake reaches the temperature of 39.2° Fahr., and is, there- 
fore, as heavy as it can get by loss of heat, as the water 



THE NATURE OF HEAT 



233 



near the surface continues to lose its heat, it grows lighter 
and remains at the surface until changed into ice. Since 
water conducts heat poorly, the water at the bottom re- 
mains unfrozen. Were it not for this peculiarity in its 
expansion, the water throughout the lake would continue 
to cool until the whole mass became solid, when not even 
a summer's heat would entirely melt it. 

355. Expansion of Gases. — At ordinary temperatures 
and pressures, air expands about -^j of its volume for each 
degree Fahrenheit increase in temperature. At ordinary 
temperatures and pressures nearly all gases have the same 
expansion as air. 

When the earth's atmosphere is heated, it expands; 
when cooled, it contracts. When any mass of air is 
heated it expands, and, becoming lighter than the sur- 
rounding air, rises while the cooler air on the sides blows 
in towards the place from which the heated 
air has risen. Winds are caused in this way. 

The draught in a chimney is caused by the 
air within the chimney being heated and ris- 
ing, and the cooler air rushing in through the 
fire to take the place left by the rising air. 

Experiment 78. — Place a narrow glass tube fitted 
air-tight to a cork in the neck of a large bottle A, of thin 
glass. Hold the bottle for a few minutes near a gas 
flame, or a hot stove, and then quickly place it, as shown 
in Fig. 144, with the end of the tube dipping below the 
surface of some colored liquid in B. As the air in the 
bottle cools, it contracts, and the pressure of the out- 
side air causes a column of liquid to mount in the tube. 
If, however, the air in the bottle be again heated, as by 
holdiDg the hand on it, the expansion of the air will 
drive the column of colored liquid down. This appa- 
ratus will, therefore, act like a thermometer ; only the 
column of colored liquid falls when the air is warm, and 
rises when it is cold. It acts also somewhat like a barometer, since an in- 
crease in the pressure of the atmosphere will cause the column to rise, 
and a decrease in pressure will cause it to fall. 




Fig.144.-Ex- 
pansion and 
Contraction 
of Air. 







CHAPTER XX. 

COMMUNICATION OF HEAT.— SURFACE ACTION 
OF BODIES. 

356. The Communication of Heat. — Heat may be 
communicated or transferred from one body to another in 
three ways : 

(1.) By conduction. 

(2.) By convection. 

(3.) By radiation. 

Heat is communicated through solids by conduction; 
and through liquids and gases, mainly by convection and 
radiation. 

357. Conduction of Heat. — If one end of a short bar 
of iron, copper, or any other metal, be placed in a fire, the 
other end will gradually become too hot to be held in the 
hand. The heat has been communicated from the fire to 
the rod and carried through the substance of the rod by 
conduction. 

When the molecules at the heated end of the bar are set into more 
energetic motion by the heat of the fire, they gradually impart their 
increased motion to the molecules beyond them, and in this way heat 
is conducted through the bar. The rapidity of heat conduction from 
one end of a bar to the other is the same whether the bar be straight or 
bent. As a rule heat is conducted better by solids than by liquids, and 
better by liquids than by gases. 

358. Conductivity. — The rapidity with which heat is 
conducted varies greatly in different solids. If the ends 
of two rods of the same length and thickness, one of cop- 

234 



COMMUNICATION OF HEAT. 



235 



per and the other of iron, be placed in a fire, under exactly 
similar conditions, the heat will be conducted through the 
copper rod much more rapidly than through the iron rod. 
Again, if a rod of glass be similarly placed in the same 
fire, it will be found to be a very bad conductor of heat. 

Experiment 79.— Stick a number of marbles or buckshot, by means 




Fig, 145.— Unequal Conductivity of Copper and Iron. 

of wax, at equal distances apart, on two bars, A, of copper, and B, of iron^ 
of the same length and thickness, as shown in Fig. 145. Expose one end 
of each bar to the same source of heat, as, for exam- 
ple, the flame of an alcohol lamp or Bunsen burner. 
It will be observed that the balls will fall sooner from 
the copper bar than from the iron, thus showing that 
the copper bar is the better conductor of heat. 

Experiment 80. — A Bunsen burner can be easily 
made as follows : Take a piece of tin in the shape of 
a rectangle, and cut out small pieces from one of its 
shorter ends, so that, when the tin is rolled in the form 
of a hollow tube, as shown at B, Fig. 146, there will be 
openings provided as at A. Fit the end C, loosely over 
a gas-burner. Turn on the gas, and light it from above. 
If the burner has been properly made, the gas will burn 
with a faint bluish, but almost non-luminous flame, and 
will not soot articles heated in it. Air enters at the 
openings below, and burns the gas more thoroughly 
than an ordinary gas-burner. This flame is very hot ; 
glass tubes held in it will soften and may be bent in 
any desired shape. 

359. Applications of the Conductivity ^tnlS* 
of Solids. — When a cold body is placed in 
contact with a hot body it begins to abstract heat from the 
hot body. If we wish to prevent this loss of heat by the 
hot body we must surround it by some substance that 
conducts heat very poorly. 




236 NATURAL PHILOSOPHY. 

Ice is wrapped in blankets to keep it from melting, be- 
cause the blankets have a low heat conductivity, and there- 
fore prevent the heat from entering. 

Thick woollen clothes are worn in winter to keep the 
heat of our bodies from escaping rapidly. Thin muslin 
or linen clothes are comfortable in summer, because they 
readily permit the heat of the body to escape. 

Ice-houses are made with thick, double walls, filled 
with shavings or sawdust, to keep heat from entering. 
For the same purpose, fire-proof safes have double or 
triple walls, filled with some poor conductor. 

Very little of the heat of the interior of the earth 
reaches the surface, owing to the low conducting power 
of the materials forming the earth's crust. 

360. Table of Conductivity. — The differences in heat 
conductivities are shown in the table given below. 1 Here, 

1 Table of Conductivities. 

I. Metals. — (Gold as Unity.) 

Gold 1.00 Cast iron" 0.52 

Platinum 0.98 Wrought iron 0.44 

Silver ......... 0.97 Zinc 0.36 

Copper 0.89 Tin 0.30 

Brass 0.76 Lead 0.18 

II. Mineral Substances. — (Slate as Unity.) 

Coke 1.98 Glass 0.96 

Coal, anthracite 1.92 Fire brick 0.61 

Cold, bituminous . . . .1.68 Lime 0.24 

Marble 1.22 Cement 0.21 

Slate 1.00 Charcoal 0.07 

III. Materials Employed for Clothing. — (Air as Unity.) 

Air 1.00 Eiderdown 0.22 

Cotton 0.28 Silk 0.21 

Wool 0.25 Hemp canvas 0.14 

IV- Liquids. — (Water as Unity.) 

Turpentine 3.10 Water 1.00 

Mercury 2.80 Alcohol 0.93 

Sulphuric acid 1.70 Proof spirit 0.85 



COMMUNICATION OF HEAT. 



237 



as will be seen, gold, platinum, silver and copper, are rela- 
tively good conductors of heat, and zinc, tin and lead are 
poor conductors. Cotton is a better conductor than silk. 
Turpentine has about three times as high a conductivity 
as water. Alcohol has a lower conductivity than water. 

361. Conduction of Fluids. — Liquids and gases gen- 
erally are very bad conductors of heat. When heated 
from below they grow hot almost entirely by a process 
called convection; when heated from above, they conduct 
but very little heat downward, since convection cannot 
take place. 

Experiment 81. — Insert the tube of the simple thermometer, de- 
scribed in Experiment 78, through a cork, and place the cork, as shown 
in Fig. 147, in the small end A, of a funnel, the neck of which has been 
cut off. Fill the funnel with water, so as to cover the bulb B, to the 
depth of about one-quarter of an inch. Pour some ether 
on the water, and set fire to it. So little heat will be 
conducted downwards through the water, that the level 
of the column of colored water at b, will scarcely fall. 

362. Convection. — When a vessel con- 
taining a liquid is placed over a source of 
heat, the liquid touching the hot bottom 
of the vessel is heated, and expanding, be- 
comes lighter and rises, its place being filled 
by some of the cooler portions of the liquid 
falling. These in turn become heated, and 
are replaced by other portions, until at last 
the whole mass of the liquid is at the same 
temperature throughout. Heat is trans- 
ferred through gases in the same way. 

When liquids and gases are heated they 
are so stirred about by the heat, that all parts are brought 
in contact with the sides of the vessel. This method of 
communicating heat is called convection. Liquids and 
gases are cooled in a similar manner. 

Experiment 82. — Place a lump of ice in a tumbler of tepid water. 




Fig. 147 —Water 

a Poor Conductor 

of Heat. 




238 NATURAL PHILOSOPHY. 

As the water which touches the ice is cooled, it becomes heavier, and sink- 
ing, pushes the warmer and ligher water up from below. By watching 
the water closely, these currents can be seen, especially if there are any 
little specks of dirt in the water. Their general 
direction is shown in Fig. 148, by the arrows. 

During convection, the warmer portions 
of the liquid or gas always move toward 
the cooler portions, and the cooler portions 
toward the warmer portions. 
Fig. 148 — Oonvec- Winds are huge convection currents in 
the air caused by the unequal heating of 
different portions of the surface of the earth. The con- 
stant oceanic currents are huge convection currents in the 
ocean, and are caused by differences of temperature be- 
tween the water at the equator and at the poles. 

363. The Radiation of Heat. — Radiant energy ; i. e., 
the energy given off by the molecules of a heated body in 
their to-and-fro motions as wave motion in the surround- 
ing ether, may be either luminous or non-luminous. That 
is to say, a hot body will always radiate heat, but if its 
temperature is sufficiently high, some of the radiant 
energy may also be able to affect the eye as light. 

If we stand at the same distance from a cylindrical 
stove, but on different sides, we shall find, if the stove is 
formed of the same material all around and the stove-door 
is shut, that the intensity of the heat thrown out or radi- 
ated is the same in all directions. It can be shown by ex- 
periment that a spherical vessel filled with hot water will 
radiate heat equally in all directions. 

If a poker is moderately heated in a fire, it will, 
when withdrawn, radiate dark heat. If, however, it is 
more strongly heated, it will glow when withdrawn from 
the fire, that is, it will throw out not only dark heat, 
but also luminous heat. 

364. Heat Radiated in Straight Lines. — If the me- 
dium through which heat is passing be uniform through- 



COMMUNICATION OF HEAT. 239 

out, the heat which is radiated from a heated body, like 
the light radiated from a luminous body, passes off from 
it in all directions in straight lines. 

If a screen, through which heat cannot pass, be interposed between a 
thermometer and a source of heat, the thermometer will show that it is 
no longer receiving heat from the source. If, however, the screen be 
removed, the thermometer will indicate a rise in temperature. On hot 
days it is cooler in the shade than in the sunshine, because both the 
dark heat and the luminous heat from the sun move in straight lines. 

When non-luminous heat passes from one medium to 
another medium of different density, it is bent out of its 
straight course like luminous heat or light, or is refracted. 
The common burning-glass owes its power of heating 
things placed at its focus, to the fact that it is so shaped 
that both the luminous and non-luminous rays of heat 
from the sun are bent by refraction on passing through 
it, so that when they pass out, they nearly all collect at 
a single point or focus. 

365. Intensity of Radiant Heat. — The hotter a body 
is, the greater is the intensity of the heat radiated from it. 
As the molecules of a hot body have greater energy of 
motion than those of a cooler body, the energy of motion 
which the hot body communicates to the surrounding 
ether, must be greater than that communicated by the 
cooler body. 

The farther we go from a hot body, the less is the intensity of the heat 
we receive. The intensity of the heat radiated from any point of a hot 
body is inversely proportional to the square of the distance from that 
point. Generally, if we are twice as far from a hot body at one time 
as at another, the intensity of the radiant heat will be four times less. 
This decrease in the intensity of heat, with the increase of the distance, 
is similar to the decrease in the intensity of sound and light. 

366. Effects which Occur at the Surfaces of Bodies. 

— When the ether-waves emitted by a hot body strike 
against the surface of another body, they are either thrown 
back from it, absorbed by it, or transmitted through it. This 



240 NATURAL PHILOSOPHY. 

is the same in the case of luminous heat or light. The 
light which reaches a surface is thrown back from that 
surface, i. e., reflected or diffused; passes through it, as 
through glass or water; or, is absorbed by it. 

367. Reflection of Heat. — Since non-luminous heat 
differs only in frequency from light, it is to be expected 
that it obeys the same laws as light. In the case of re- 
flection, heat-waves which strike a smooth surface are 
reflected from that surface at an angle equal to the angle 
of incidence. 

Bodies vary greatly in their power of reflecting heat. 
Some bodies, like smoothly polished silver or gold, will 
reflect a large part of the heat which falls upon them, 
while others, like a rough, soot-covered surface, will re- 
flect but little heat. As a rule, bright polished metallic 
surfaces are good reflectors of heat. 

Experiment 83.— Hold a brightly-polished piece of tin in front of 
an open fire, so as to reflect the light and heat. Notice that the spot 
where the patch of light reflected from the tin falls, is warmer than the 
space around it, thus showing that the non-luminous heat of the fire is 
reflected as well as the light. Hold the tin so that the light of the fire is 
thrown into the face, and an increase of temperature will at once be felt. 

368. Absorption and Radiation of Heat. — The ether- 
waves that are not reflected from the surface of the body 
on which they fall, enter its substance, and are either 
absorbed, i. e., give their to-and-fro motions to the mole- 
cules of the body, thereby making the body hot, or they 
pass through the body without heating it, merely giving 
their motion to the ether between the molecules. 

When a body has absorbed heat and has thus become hot, it may part 
with its heat by radiation ; that is, it may set the ether surrounding it, 
into wave motions, by a process sometimes called secondary radiation. 

If a body is a good absorber of heat, it must also be a 
good radiator or emitter of heat. Lampblack is both a 
good absorber and a good radiator of heat. 

If a body is a good reflector of heat, that is, if it throws 



COMMUNICATION OF HEAT. 241 

off most of the ether- waves from its surface, it cannot, of 
course, take them in, or be a good absorber. 

Anything, therefore, which increases the reflecting power 
of a body must decrease both its absorptive and radiating 
power. Anything which increases the absorptive or radiat- 
ing power of a body must decrease its reflecting power. 
Thus, smoothing and polishing diminish the absorptive 
and radiating powers, but increase the reflecting power. 
The opposite effects are produced by roughening or dull- 
ing a surface. 

Bodies are continually radiating or losing their heat, no matter 
whether their temperature be the same as, or different from, the tem- 
perature of surrounding bodies, and thus tend to become lower in tem- 
perature, and to absorb the heat that falls on them from other bodies. 
When their temperature remains constant, it is because the quantity 
of heat they radiate and the quantity of heat they absorb are the same 
in any given time. 

369. Applications of Absorptive, Emissive, and 
Reflecting Powers. — Coffee and tea are brought to the 
table in highly polished pots, which, being good reflectors 
of heat, are bad radiators. The contents of such pots will, 
therefore, keep warm for a greater length of time than if 
their outsides were rough and dull. 

Meat roasters are so arranged that the radiant heat of 
the fire is reflected from the surfaces of brightly polished 
tin, on the meat to be cooked. 

If the outside of a stove be too brightly polished, much 
less of its heat will be radiated into the room than if the 
outside were rough and dull. 

370. Selective Absorption and Selective Radia- 
tion. — When light falls on the surface of a body it may, 
like heat, either be thrown off at the surface, transmitted 
through the substance, or absorbed by it. Colored bodies 
possess the power of throwing off light of a particular color 
only. White bodies can throw off light of all colors. A 
colored, transparent body permits the light of only cer- 

16 v 



242 



NATURAL PHILOSOPHY. 



tain colors to pass through it and is opaque to all other 
colors. A transparent, colorless body, like a sheet of clear 
glass, is transparent to light of all colors. The light rays 
to which a colored body is opaque, are absorbed and may 
appear as heat. It is evident, in the case of light, that 
the ability of a body to throw off or radiate light or to 
take in or absorb light, will vary with the color of the 
light, and, therefore, with the source of the light. In a 
similar manner the ability of a substance to throw off or 
radiate heat varies in a marked manner with the nature 
of the source of heat. Like a plate of red glass, which is 
transparent to red light, but opaque to blue light, a body 
may be transparent to much of the heat emitted by an 
incandescent platinum wire, although it is opaque to the 
heat emitted by a vessel filled with boiling water. 

In the table below 1 are given the absorptive and re- 
flecting powers of different substances. The reflecting 
power as given in this table includes both the regularly 
reflected and the diffused rays. 

371. Cause of Selective Absorption. — We have seen 
that sound-waves, striking against the strings of a piano, 
may give part of their motion to the strings, provided the 



1 Radiating and Absorbing 

Substance. 

Absorp- 
tion. 
Lamp-black . . . .100 

Water 100 

Carbonate of lead . 100 
Writing paper ... 98 

Eesin 96 

Glass ...... 90 

India ink 85 

Ice 85 

Lead, dull .... 45 
Polished iron ... 25 
Mercury 23 



Powers of Various Substances. 





Substance. 




Reflec- 




Absorp- 


Reflec- 


tion. 




tion. 


tion. 


— 


Polished lead . . 


. 19 


81 


— 


Polished zinc . • 


. 19 


81 


— 


Polished steel . . 


. 17 


83 


2 


Platinum, sheet . 


. 17 


83 


4 


Tin 


. 15 


85 


10 


Copper, varnished 


. 14 


86 


15 


Brass, dead polishe( 


1 11 


89 


15 


Brass, bright . . 


. 7 


93 


55 


Copper, polished 


. 7 


93 


75 


Gold, polished . . 


. 3 


97 


77 


Silver, polished . 


. 3 


97 






COMMUNICATION OF HEAT. 243 

strings can vibrate at the same rate as the sound-waves 
which strike them ; or, in other words, sound-waves excite 
sympathetic vibrations in the strings. The same is true 
with the ether-waves. If they strike against a body, 
whose molecules are able to vibrate at the same rate as 
the ether w T aves, the heat is said to be absorbed, since the 
molecules are set into vibration. Otherwise, the ether- 
waves may simply pass through the body by setting the 
ether between the molecules into motion. 

372. Diathermancy. — When the ether- waves pass 
through a body without heating it, that is, when they 
pass through a body without imparting their motion to 
its molecules, the body is said to be diathermanous, or 
transparent to heat. When it will not let the heat so pass 
through, it is said to be athermanous, or opaque to heat. 
In diathermanous bodies the ether-waves impart their 
motion to the ether between the molecules. 

Clear rock salt is diathermanous to all kinds of heat. 
Dry air is diathermanous, but when it contains water- 
vapor is less diathermanous. It is mainly to the vapor 
of water our atmosphere contains, that it owes its power 
of absorbing a part of the sun's heat. 

Diathermancy is independent of transparency. Thus 
alum freely allows light to pass through it, but stops non- 
luminous heat ; while smoky quartz, which is almost opaque 
to luminous heat, allows heat to pass through it readily. 
A solution of iodine in bisulphide of carbon, is opaque to 
luminous heat or light, but transparent to non-luminous 
heat. 

Experiment 84. — Hold a piece of clean window glass between the 
face and the open door of a fire, and observe that the face feels cooler 
when shielded by the glass. The glass is opaque or athermanous to 
the heat of the fire. Now hold the glass between the face and the sun, 
and no perceptible difference will be felt in the heat, whether the face be 
shielded by the glass or not ; the glass, therefore, is diathermanous to 
the sun's heat. 




CHAPTER XXI. 

HEAT UNITS.— CHANGE OF STATE.— MECHANICAL 
EQUIVALENT OF HEAT. 



°o>Ko* 

373. Heat Units. — The total quantity of molecular or 
heat energy present in any substance cannot be determined 
when only its temperature is known. A thermometer, 
plunged into a cup full of boiling water, would indicate 
the same temperature; viz., 212° F., as if plunged into a 
tub full of boiling water ; although, manifestly, the quan- 
tity of heat energy present in the latter case is much 
greater than in the former. To determine the quantity 
of heat energy present in any case we must know : 

(1.) The kind of substance. 

(2.) The quantity of the substance ; i. e n its weight in 
pounds or grammes. 

(3.) The temperature of the substance in degrees. 

The quantity of heat energy is measured in units called 
heat units. Two heat units are commonly employed : the 
pound-degree-Fahrenheit, and the gramme-degree- Centigrade, 
or the small calorie; the former is the amount of heat 
required to raise the temperature of one pound of water, 
1° F. The latter is the amount of heat required to raise 
the temperature of one gramme of water, 1° C. 

If, in the case alluded to above, the cup contained, say 
one pound of water, and the tub, 1000 pounds, the quan- 

244 



HEAT UNITS.— CHANGE OF STATE. 



245 



tity of heat present in the water in the tub would be 1000 
times greater than the quantity of heat present in the 
water in the cup, provided both were at the same tem- 
perature. 

374. Specific Heat. — Equal quantities of different sub- 
stances are not raised to the same temperature, by equal 
quantities of heat. If we add the same amount of heat 
energy to a pound of mercury, and to a pound of water, 
we shall find that if the water has been heated one degree, 
the mercury will have been heated thirty-three degrees. 
We conclude, therefore, that a given weight of water has 
thirty-three times the capacity for heat that an equal 
weight of mercury has. 

The specific heat of a substance is the amount of heat 
required to raise the temperature of a given quantity of 
that substance, through a certain number of degrees, as 
compared with the amount of heat required to raise an 
equal quantity of some other substance through the same 
number of degrees. Water, which possesses the highest 
specific heat of any common substance, is generally adopted 
as the standard of comparison. 

The specific heat of a substance varies with its con- 
dition. The same substance has a greater specific heat in 
the gaseous state than in the liquid state, and a greater 
specific heat in the liquid state than in the solid state. 

In the table given below, 1 the specific heats of various 

Specific Heats. (Equal Weights.) 



Water 1.000 

Vinegar 0.920 

Alcohol 0.659 

Ice 0.504 

Marble 0.270 

Phosphorus 0.250 

Charcoal 0.242 

Sulphur 0.213 

Steel 0,117 



Iron, wrought 0.114 

Nickel 0.109 

Zinc 0.096 

Brass 0.094 

Copper 0.092 

Tin 0.056 

Silver 0.056 

Mercury 0.033 

Platinum 0,032 



246 



NATURAL PHILOSOPHY. 



substances are given, compared with water at 32° F. as 
unity. 

375. The Calorimeter. — There are various methods 
for ascertaining the specific heat of any substance. Those 
most in use are : 

(1.) By means of an instrument called a calorimeter. 

(2.) By the method of mixture. 

The calorimetric method is based on ascertaining how 
much ice a given weight of a substance will melt, in cool- 
ing from a known temperature to that of 
melting ice. The calorimeter consists of 
three hollow vessels, M, A, i>, placed in- 
side one another, as shown in Fig. 149. 
The vessels A and B, are packed with 
dry ice. The substance, whose specific 
heat is desired, is placed in if, and in 
cooling, melts the ice in A, the quan- 
tity melted being inferred from the water 
which runs into D. The ice in B, pre- 
vents the heat of the outer air from melt- 
ting any of the ice in A. 

Suppose one pound of a given substance, heated 

to 212° F., is placed in if, and in cooling to 32° 

F. , only melts half as much ice as a pound of water would in cooling 

through the same range ; i. e., from 212° to 32° : then the specific heat 

of the body is J = .5. 

376. The Method of Mixture consists essentially in 
mixing together either equal weights, or equal volumes, of 
the substance whose specific heat is to be ascertained, and 
carefully noting the temperature of the mixture. 

Suppose, for example, that one pound of water at 156° F., is mixed 
with a pound of mercury at 40° F., and that the resulting temperature 
is 152.3° F. Here the water loses 3.7° F., and the mercury gains 112.3° 
F. ; or, in other words, 3.7 water-pound-degrees-Fahrenheit equal 
112.3 mercury-pound-degrees-Fahrenheit ; or, 112.3: 3.7 : : 1 : the spe- 
cific heat of mercury ; or, the specific heat of mercury is 0.033, 




Fig, 149 -The Ca- 
lorimeter. 



HEAT UNITS.— CHANGE OF STATE. 247 

377. The Specific Heat of Water. — Water has a 
higher specific heat than almost any other common sub- 
stance, that is, it takes in more heat when being warmed, 
and gives out more heat when being cooled, than any otfrer 
common substance. Since about three- fourths of the earth's 
surface is covered with water, it is evident that the high 
specific heat of water must exert a great influence in pre- 
venting extremes of temperature, since water can absorb 
or emit considerable heat without much change in tem- 
perature. 

378. Latent Heat.— When a pound of ice at 32° F. is melted, the 
water which comes from it is still ice-cold, or at 32° F. All the heat 
which has been imparted to the ice to melt it, has disappeared as heat ; 
or, as it is called, has become latent. The pound of ice at 32° F. has 
been converted into a pound of water at 32° F., by the expenditure of 
a certain amount of heat energy. When this pound of water is frozen 
all this latent heat becomes sensible. 

When a pound of water is vaporized at 212° F., the steam which 
comes from it is still at 212° F., or is no hotter than the water. All the 
heat which has been given to the water to vaporize it, has disappeared 
as heat ; or, as in the case of melted ice, has become latent. The 
pound of water at 212° F. has become converted into a pound of steam 
at 212° F., by the expenditure of a certain amount of heat energy. 
When the steam is condensed, all this latent heat becomes sensible. 

When a solid melts, or when a liquid vaporizes, heat energy disap- 
pears and ceases to exist as heat energy. This energy is expended in 
effecting the change of state or condition of che substance ; t. e., in doing 
internal work on the body. In other words, the kinetic molecular en- 
ergy or heat is converted into potential molecular energy. Potential 
molecular heat energy was formerly called latent heat, and the word is 
to some extent, still employed. The term is, however, misleading. 
Strictly speaking, such energy is not heat energy, though, like other 
forms of energy, it is capable of becoming changed into heat energy. In 
point of fact, when a fused substance solidifies, or a vapor condenses, 
the potential molecular energy appears as heat. The amount of heat 
energy required to fuse a given weight of a solid substance, or to vapor- 
ize a given weight of liquid substance, differs with different substances, 
but it is always the same with the same substance under the same cir- 
cumstances. 



248 NA TUBAL PHILOSOPHY. 

Experiment 85. — So place one pound of ice at 32° F., and one 
pound of water at 32° F. in separate vessels, over the same source of 
heat, that each will receive the same quantity of heat. When all the ice 
is melted, plunge a thermometer in the water in each vessel, and observe 
that the ice- water has now a temperature of about 174° F., and the water 
from the melted ice has only a temperature of 32° F. Similarly, one 
gramme of ice at 0° C. would require about 79 calories to change it into 
water at 0° C. 

Since, in the preceding experiment, 142 pound-degrees- 
Fahrenheit, or 142 British heat units, have disappeared, it 
is evident that this quantity of heat is required in order 
to change a pound of ice, at 32° F., into a pound of water 
at 32° F. Conversely, when a pound of water at 32° F. 
freezes, 142 British heat units are given out ; and, in order 
to freeze a pound of water at 32° F., this quantity of heat 
must be taken from the water. 

379. Laws of Fusion. — It can be shown experiment- 
ally that the following laws govern the fusion of bodies : 

(1.) Under the same pressure, every substance capable 
of fusion, has a fixed temperature at which it begins to 
fuse. 

(2.) When any substance begins to fuse, the tempera- 
ture remains constant until all the substance is fused. 

Ice begins to fuse at the temperature of 32° F. If ice be placed in 
a vessel over a source of heat, a thermometer plunged in the water 
which comes from the melting ice, will remain at the same tempera- 
ture, 32° F., until all of the ice is melted. 

380. Laws of Solidification. — Bodies which have been 
fused by heat, solidify when sufficiently cooled. Solidifi- 
cation is the reverse of liquefaction. The laws of solidi- 
fication are similar to those of fusion ; they are as follows : 

(1.) Under the same pressure, every substance solidifies 
at the same temperature as that at which it fuses. 

(2.) When the solidification has begun, the temperature 
remains constant, until all the substance has solidified. 

Water begins to freeze at 32° F., the temperature at which ice begins 
to melt. When a body of water which has been cooled to 32° F. begins 



HEAT UNITS.— CHANGE OF STATE. 



249 



to freeze, the temperature of the water will remain at 32° F. until it is 
all frozen no matter how intense the cold. 

In the table given below will be found the temperatures 
of the melting-points of different substances. 1 

381. Effect of the Freezing of Water on the Tem- 
perature of the Air. — A large body of water cannot be 
cooled below the temperature of 32° F., until the entire 
mass has been changed into ice. During the change from 
water to ice, a large quantity of energy in the water is 
liberated in the form of heat. Consequently, the freezing 
of large bodies of water tends to raise the temperature of 
the surrounding air. 

Both freezing and melting are gradual processes, be- 
cause heat disappears when ice melts, and reappears when 
water freezes. 

382. Freezing Mixtures.— Considerable heat disap- 
pears during the change of a solid into a liquid by solu- 
tion. Hence, when solids are rapidly dissolved in a liquid, 
a marked cooling occurs. In some cases the liquid is 
warmed; here, however, a chemical combination occurs 
between the solid and the liquid, and more heat is pro- 
duced than is absorbed during the solution. 

Advantage is taken of the cooling produced by the solu- 
tion of solids to obtain low temperatures artificially. Freez- 
ing mixtures consist of mixtures of different solids, or of 



1 


Melting-Points of 


Various Substances. 






Degrees 
Fahr. 


Degrees 
Cent. 




Degrees 
Fahr. 


Degrees 
Cent. 


Iridium . . 


. 3542 


1950 


Aluminum . 


. . 1157 


625 


Platinum . 




3227 


1775 


Zinc . . . 


. . 779 


415 


Iron . . . 




2822 


1550 


Lead . . . 


. . 619 


326 


Steel . . . 




2462 


1350 


Tin ... . 


. . 455 


235 


Gold . . . 




2156 


1180 


Ice .... 


. . 32 





Cast iron 




. 2012 


1100 


Mercury . . 


. . -39 


-39.5 


Copper . . 




1929 


1054 


Alcohol . . 


. . -202 


-130 


Silver . . 




1733 


945 


Oxygen . . 


. . -296 


-182 



250 NA TUBAL PHILOSOPHY. 

different liquids and solids, which, when mixed, will dis- 
solve, and so cause a reduction of temperature. By their 
use very low temperatures can be obtained. 

A simple freezing mixture consists of one part of salt, 
and two parts of ice or snow, spread in alternate layers. 
With this mixture, a temperature as low as 5° F., can be 
obtained. Freezing mixtures are used in the preparation 
of ice-cream. The material to be frozen is put in a tin 
vessel, placed inside a larger vessel of wood. Salt and ice 
are packed in layers in the space between the two vessels. 
The salt causes the ice to melt rapidly, the heat necessary 
for the melting of the ice being taken from the cream, 
which is thus frozen. The outer vessel is made of some 
bad conductor of heat, such as wood, in order to prevent 
the ice obtaining heat from the air. 

383. Increase of Volume during Solidification. — 

Some metals, such as mercury, contract on solidifying. 
It is for this reason that the freezing of the mercury in 
the bulb of a thermometer does not burst it. Other metals, 
like antimony, expand on solidifying, and hence fill the 
moulds into which they have been poured, and so take 
sharp casts. Type-metal, an alloy consisting of three 
parts of lead and one of antimony, owes its power of 
taking sharp casts of the type to its expansion on so- 
lidification. Water expands with considerable force on 
freezing. Tubs filled with water are often burst during a 
cold night ; even iron bomb-shells have been burst by fill- 
ing them with water, and then exposing them to a freezing 
temperature. 

The water, which is absorbed by porous rocks, or which runs into the 
crevices of those of more compact structure, may expand on freezing 
with sufficient force to break the rocks into fragments. In this manner 
water disintegrates or breaks down the rocks, and thus aids the rivers in 
carrying the mountains piecemeal toward the ocean. 

384. Vaporization. — Nearly all liquids, when suffi- 






HEAT UNITS.— CHANGE OF STATE. 251 

ciently heated, are vaporized or changed into vapors. 
When the vapor passes off from the surface only of the 
liquid, the liquid is said to evaporate; when the vapor is 
given off also throughout the mass, the liquid is said to 
boil. Some solids pass into a state of vapor without ap- 
pearing first to become liquids ; they are then said to be 
sublimed. Arsenic and camphor are examples of such a 
solid. 

385. Formation of Vapors in a Vacuum. — A vola- 
tile liquid, when placed in a vacuous or empty space, 
rapidly vaporizes or passes into a vapor without the ad- 
dition of external heat. 

A drop of any volatile liquid, if passed up into the empty space above 
the mercury of a thermometer tube, will disappear and turn into vapor. 
At the same time the vapor will more than fill the vacuum, that is, it 
will depress the mercury column, thus showing that it possesses tension. 
If more liquid be passed into the tube, it also will evaporate, and the col- 
umn of mercury will be further depressed ; but, after a certain amount 
of vapor has been formed, the amount depending on the temperature, 
the mercury column will remain stationary, and no more liquid will be 
evaporated. If more liquid be passed into the tube, it will simply float 
on top of the mercury. The vapor in the tube is then at its maximum 
or greatest tension, and the space it occupies is said to be saturated with 
vapor. If now, the tube be heated, more of the liquid will evaporate, 
and the mercury will be further depressed. 

386. Circumstances Influencing Evaporation. — 

The rapidity with which a liquid evaporates, depends : 

(1.) On the extent of the surface exposed ; because 
evaporation takes place at the surface. 

(2.) On the quantity of the same vapor already present 
in the air; because, when the air is saturated, no more of 
the liquid can evaporate. 

(3.) On the removal of the air ; because evaporation 
ceases when the air over the liquid is saturated ; if, how- 
ever, fresh air is brought to the surface, more liquid evap- 
orates. 



252 NATURAL PHILOSOPHY. 

(4.) On the temperature ; because warm air can hold 
more vapor than cold air. 

(5.) On the pressure on the surface ; because the greater 
the pressure the less the evaporation. In a vacuum all 
vaporizable liquids rapidly vaporize. 

In drying clothes, they are spread out on lines rather 
than rolled up. It is known that clothes dry more rapidly 
on a warm day when the wind blows, than on a cold day 
when the air is still. 

A pint of water poured into a narrow-necked bottle, will 
evaporate less rapidly than a pint of water poured into 
a plate, and this in its turn will evaporate less rapidly 
than a pint of water sprinkled upon the surface of a sheet. 

387. Laws of the Boiling of Liquids. — The laws for 
the boiling of liquids are similar to those for the fusion of 
solids. They may be expressed as follows : 

(1.) The pressure remaining the same, there is for every 
liquid a certain temperature at which it boils. 

(2.) When a liquid has been heated to the boiling-point, the 
temperature remains the same until all the liquid has been vapor- 
ized. All the heat a liquid receives, after it has once reached 
its boiling-point, is rendered latent in converting the liquid 
into vapor. 

In the table given below, the boiling-points of a few 
substances are given. 1 

388. Influence of Pressure on the Boiling-Point. — 

Before a liquid exposed to the air can boil, its vapor 
must possess a tension sufficient to enable it to overcome 

1 Boiling-Points. 

Degrees Degrees Degrees Degrees 

Fahr. Cent. Fahr. Cent. 

Ether 95 35 Benzine .... 177 80.5 

Ammonia , . . 140 60.0 Mercury .... 676 358 

Alcohol .... 173 78,3 Linseed oil . . . 729 387,5 



HEAT UNITS.— CHANGE OF STATE. 



253 



the- pressure of the air. Hence, the tension of the vapor' escap- 
ing from a boiling liquid is equal to the pressure of the atmos- 
phere. If, therefore, the pressure on a liquid is increased, 
the tension of its vapor must be increased before the liquid 
can boil ; that is, the temperature of the liquid must be 
increased. 

A liquid can never be raised above the temperature of 
its boiling-point while its vapor is allowed to escape into 
the air. If the vapor be confined, the pressure on the sur- 
face is increased, and the temperature can be increased to 
any extent, provided the vessel is sufficiently strong. To 
extract glue from bones, they are boiled at very high tem- 
peratures, in water placed in closed vessels provided with 
safety-valves for the escape of the steam, should the pres- 
sure become too great. 

That the temperature of a vessel does not rise above 
the boiling-point may be shown by the following curious 
experiment. 

Experiment 86. — To boil water in a paper bag. Take a square piece 
of paper and fold it so as to form a conical bag A, as shown in Fig. 150. 
Suspend the hag by strings, and pouring water into it, 
allow the flame of an alcohol-lamp, or Bunsen burner, 
to fall on the bag, being careful to prevent the flame 
from touching the paper in any place where there is 
no water. The water can now be heated until it boils, 
without the paper being burned, because the paper 
cannot be heated much more than 212° F., and this is 
not suflicient to burn it. 

Experiment 87.— That a diminished pressure 
lowers the boiling-point may be shown by an experiment 
sometimes called the culinary paradox. Water is boiled 
in a suitable glass flask A, Fig. 151, and after a few 
minutes of vigorous boiling, so as to permit the steam 
formed to drive all the air out of the flask, the source 
of heat is removed, and the neck is closed by a tightly 
fitting cork, which has been previously steeped in 
melted wax or paraflin, so as to fill all its pores. The vessel is now in- 
verted with its neck below a water-surface C, in order to prevent the 
entrance of air. For a few moments the water will continue to boil ; but 
the increased pressure on the surface, produced by the confined vapor, 

W 




Fig. 150, — Water 
Boiled in a Paper 



254 



NATURAL PHILOSOPHY. 




Fig. 151 —The Culinary 
Paradox. 



soon raises the boiling-point and stops the boiling. Now let some cold 
water fall on the bottom of the flask, as shown. The vapor will 
then be condensed, and the pressure being 
diminished, the liquid bursts into vigorous 
boiling. Pour hot water on the flask and it- 
will again stop boiling. 

389. Influence of Adhesion on 
the Boiling - Point. — Solids dis- 
solved in a liquid increase the tem- 
perature of its boiling-point. Thus 
water, containing as much salt as it 
will hold, boils at the ordinary pres- 
sure at 227° F. or 108.3° C. 

Distillation is a process by which 
a liquid can be separated from a 
solid dissolved in it. The vapor 
w T hich escapes from a liquid con- 
taining a solid in solution, does not carry the solid with 
it. If, therefore, we boil the solution, and condense the 
vapor as it escapes, we separate the liquid from the solid. 
The vapor from boiling ocean water, when condensed, 
yields water entirely free from salt. Rain is due to con- 
densation water evaporated mainly from the ocean. 

The pressure remaining the same, the boiling-point varies slightly 
with the nature and shape of the vessel in which the liquid is boiled ; 
because the vapor cannot escape until the adhesion of the liquid to the 
vessel is overcome. 

390. Heat of Vaporization. — The amount of heat 
expended during the change of one pound of water at 
212° F. into steam at 212° F., is sufficient to raise the tem- 
perature of about one thousand times as much water 1° F. ; 
or, is equal to 1000 heat units; or, 1000 pound-degrees 
Fahrenheit. The amount of heat required to convert one 
gramme of water at 100° C. to vapor, is 536 calories. 

When vapor loses heat and condenses, the latent heat 
again appears as sensible heat. Thus, large buildings are 



Heat units.— change of state. 255 

frequently warmed in winter by the exhaust steam from 
a steam engine. The steam is passed through pipes, and, 
as it condenses in these pipes, it gives out its latent heat. 

391. Reduction of Temperature Caused by Evap- 
oration. — We are cooled by fanning, because the warm 
air, thus brought into contact with the skin, causes a rapid 
evaporation of the moisture of the skin, and thus lowers 
the temperature. 

If water be placed in a vacuous space, and the vapor which escapes 
from it is removed as rapidly as it is formed, the water will be frozen 
by its own evaporation. Ice machines are constructed on this prin- 
ciple. The water must take in heat in order to evaporate, and this heat 
is taken from the rest of the water, which is thus frozen. 

When water evaporates at temperatures below the boiling-point, a 
still greater amount of heat disappears. During the change of water 
into vapor by the heat of the sun, more than 1000 heat units per pound 
of water, or water vapor, are absorbed. This heat again becomes sensible 
as the water condenses. Since much of this condensation takes place in 
cold countries, we can see that such countries must be made warmer by 
means of the rain or snow which falls in them. 

392. Mechanical Equivalent of Heat. — Energy can 
never be annihilated. When it disappears in one form it 
invariably reappears in some other form. Heat is one of 
the commonest forms into which mechanical motion can 
be changed ; for, since heat is an effect produced by the 
vibrations or shakings of the molecules of bodies, we can 
easily change mechanical motion into heat. This fact was 
first discovered by Benjamin Thomson, an American, now 
generally known as Count Rumford. 

As the result of many accurate experiments, we know 
the exact amount of mechanical force necessary to pro- 
duce a given quantity of heat. 

The work necessary to produce sufficient heat to raise 
the temperature of one pound of water 1° Fahr., is equal 
to that expended by a weight of 777 lbs., falling through 
the space of one foot. Conversely, one pound of water, 
cooling through 1° Fahr., gives out a quantity of heat, 



256 NATURAL PHILOSOPHY. 

which, could it be utilized, would be capable of exerting 
a mechanical force sufficient to raise 777 lbs., through the 
space of one foot. These figures were first determined by 
an Englishman named Joule, and are called Joule's equiva- 
lent 

The fact that heat can be produced by mechanical work 
is seen in the heat developed by the friction of one surface 
on another, and also in the heat developed by percussion. 
A stout copper wire, if rubbed with a piece of stiff paper, 
may be made hot enough to set fire to a match ; or a soft 
iron nail may be made sufficiently hot, by rapid hammer- 
ing, to light a fire. 

393. The Steam Engine. — The method most com- 
monly adopted for the change of heat into mechanical 
work, is by means of the steam engine. (Fig. 152). 

The heat is employed to change water into steam. The 
water is placed in a suitable vessel, made of steel, called 
the boiler, the construction of which varies with the cha- 
racter of the steam engine with which it is to be used. 
The steam passes from the boiler through a pipe leading 
to a box called the steam chest, through which, by a con- 
trivance called the slide valve, it is admitted alternately 
to different sides of a piston, so arranged as to move freely 
in the cylinder D. 

By the pressure which the steam exerts, the piston is 
moved backward and forward from one end of the cylin- 
der to the other. The motion of the piston is communi- 
cated by means of the piston rod E, to a connecting-rod 
F, by which the motion is carried to a large heavy wheel 7, 
called the fly-wheel. The alternating motion of the piston 
rod is converted into a steady rotary motion by means of 
a crank /. In this manner the backward and forward 
motion of the piston produces a continuous rotary mo- 
tion of the fly-wheel. Pulleys are usually attached to the 




17 



258 NATURAL PHILOSOPHY. 

axis of the fly-wheel, from which, by means of belting 
and shafting, the motion is carried to the machinery to be 
moved. 

By means of the slide-valve the steam in the steam- 
chest is alternately cut off from one side of the piston and 
admitted to the other side, and at the same time an open- 
ing is provided through which the steam may escape from 
that side of the piston from which the steam has been cut 
off. In the condensing steam-engine this steam passes through 
a pipe into a chamber called the condenser. In this 
chamber a jet of cold water is allowed to play. By this 
means the steam, which passes from the steam cylinder 
into the condenser, is condensed, thereby lowering the 
pressure on that side of the piston from which the steam 
has just been cut off. A pump, called the air-pump, re- 
moves the water from the condenser. The slide-valve is 
moved by means of a bent lever moved by an eccentric 
rod. 

In the non-condensing engine, the steam escapes at once 
into the air, after it has moved the piston to either end of 
the cylinder. The puffs of steam which escape from such 
engines denote the speed with which the piston is being 
driven backward and forward. 

When the piston is at the farthest part of its stroke ; 
that is, when it is at either end of the cylinder, the crank 
J, and the connecting-rod F, are in the same straight 
line. In this position the motion of the piston will not 
be carried through the connecting-rod and crank so as to 
produce a rotation of the fly-wheel. These two positions 
are called the dead points of the engine. The fly-wheel by 
its inertia continues to move and carries the crank past 
these points. 

Steam engines and boilers form the mechanism by which, at the pres- 
ent time, mechanical power is generated from coal. Considering the heat 
which is liberated by the combustion of coal in air, the amount of power 
which can be developed by the best engines and boilers is comparatively 






HEAT UNITS.— CHANGE OF STATE. 259 

small. This is due to the fact that the engine works with steam and 
that water must be vaporized to form the steam, thereby wasting the 
heat of vaporization. Moreover, even a perfect steam engine would be 
unable to convert all the heat energy of steam into mechanical energy. 
From both causes combined, the best steam engines and boilers fail to 
utilize at least 85 per cent., and can develop only about 15 per cent, 
of the power equivalent to the heat produced by the coal they burn. 

394. Other Sources of Heat. — Besides the sources 
of heat already mentioned, we have heat of the sun and of 
the fixed stars, and that produced by chemical combination 
and by electricity. 

The manner in which heat is produced by chemical 
combination is well illustrated by the case of a body burn- 
ing in the air. As the combustible body combines with 
the oxygen of the air, the oxygen, in rushing toward the 
combustible materials, sets its molecules into a vibratory 
motion which causes the heat. 




CHAPTER XXII. 

ELECTROSTATICS. 



-<x>v*:o 



395. The Nature of Electricity.— Though little is 
known of the real nature of electricity, yet so much is 
known of the laws in accordance with which its phe- 
nomena are manifested, that electricity may fairly be re- 
garded as accurate a science as mechanics. Whatever be 
the nature of electricity, all other forms of energy may 
readily be converted into electric energy. 

396. Electro-Motive Force. — Whenever any other 
form of energy is converted into electric energy, a variety 
of force is produced, called electro-motive force, which is 
capable of setting electricity in motion. For convenience, 
the words electro-motive force are usually contracted 
E. M. F. Any device by means of which an E. M. F. 
is produced is called an electric source. A voltaic cell, a 
dynamo-electric machine, or a frictional electric machine, 
is an example of an electric source 

397. The Electric Circuit. — If the ends of a conduct- 
ing wire ABC, Fig. 153, are connected to the + and -- ter- 
minals of an electric source, as, for example, the voltaic 
cell shown, the E. M. F. of the cell will cause an electric 
current to flow from one pole of the cell, through the con- 
tinuous conducting path or circuit, and back again to the 
cell at its other pole. 

260 



ELECTROSTATICS. 



261 



A circuit is made, closed, or completed, when it is con- 
tinuous throughout. It is broken, open, or incomplete, when 
a break exists in any portion of its path. 

The points or places in an electric source at which the 
electricity is assumed to leave and enter the source, are 




Fig. 153.— An Electric Circuit, 

called the poles or terminals. It is agreed, for convenience, 
to consider the electricity as leaving an electric source at 




-i> 



Fig, 154,— A Hydraulic Circuit, 



its positive, or + pole, and as re-entering it at its negative, 
or —pole, as indicated by the arrows in Fig. 153. 



262 NATURAL PHILOSOPHY. 

398. The Hydraulic Circuit. — The flow or passage of 
electricity in a circuit is not unlike the flow of water 
through a pipe or system of pipes. Thus, let P, Fig. 154, 
be a centrifugal pump, driving water out of the pump at 
the opening a, through the circuit of water pipe A C B, 
and taking it again into the pump, at the opening b, 
the flow of water through the circuit being in the direc- 
tion indicated by the arrows. Here the pump produces 
a water-motive force, or force causing a motion of the water, 
corresponding to the electro-motive force produced by the 
electric source. 

It should be remembered that the above analogies between the hy- 
draulic and the electric circuits are analogies only. In the hydraulic 
circuit there is a real flow of a gross material, water. In the electric 
circuit there is no flow of a gross material. 

399. The Electric Current. — In a hydraulic circuit 
the flow, or quantity of liquid that passes in a given time, 
depends on the value of the water-motive force, or pres- 
sure acting on the liquid. The greater the force, the 
greater is the flow. So, in the electric circuit, the strength 
of the electric current that flows, depends on the strength 
of the E. M. F. ; the greater the E. M. F., the greater is the 
strength of the electric current that flows. 

In a hydraulic circuit the flow depends on the size 
and length of the pipes forming the circuit, because these 
quantities determine the hydraulic resistance, or the oppo- 
sition the pipe or circuit offers to the passage of the liquid. 
The greater the diameter of the pipe, the less will be 
the resistance it offers, and, therefore, the greater will be 
the flow. The greater the length of the pipe, the greater 
will be the resistance, and, therefore, the less will be the 
flow. 

In an electric circuit the current or electric flow de- 
pends on the size, length and character of the conducting 
substances forming the circuit, because these quantities de- 
termine the electric resistance, or the opposition the circuit 



ELECTR OSTA TICS. 263 

offers to the passage of electricity. In the case of a wire, 
the greater the diameter of the wire ; or, the greater its 
area of cross section, the less will be its resistance, and 
the greater will be the flow or current produced by a 
given E. M. F. The greater the length of the conducting 
circuit, the greater will be the resistance, and the less will 
be the current. 

In the hydraulic circuit, provided the inside of the pipe 
is smooth, the kind of material of which the pipe is com- 
posed has but little influence on the value of the flow or 
current. In the electric circuit, the nature of the material 
of which the circuit is formed has much to do with the 
resistance it offers ; and, consequently, with the value of the 
current which a given E. M. F. can cause to pass through 
the circuit. 

Substances, even when of equal lengths and areas of 
cross section, differ very considerably in the resistance 
they offer to the flow of electricity through them. Gen- 
erally, the metals are good conductors, or possess a low 
electric resistance. Hard rubber, shellac, glass and dry 
air, are bad conductors, or possess a high electric re- 
sistance. The metals, though usually good conductors, 
differ greatly in their conducting power. Copper is one 
of the best of the metallic conductors, and is, therefore, 
usually employed in electric circuits. The resistance 
of an iron wire, of a given size and length, is about 
six times that of a copper wire, of the same size and 
length. 

400. Ohm's Law. — The law in accordance with which 
electricity flows, or passes through a circuit, was discovered 
by Dr. Ohm, of Berlin, and is known as Ohm's law. It 
may be expressed as follows: 

The current which passes through any circuit is directly 
proportional to the E. M. F. acting on that circuit, and in- 
versely proportional to the resistance of the circuit; or, in 



264 NATURAL PHILOSOPHY. 

other words, the current strength increases as the E. M. F. 
increases, and diminishes as the resistance increases. 

Ohm's law is true only in cases where the E. M. F. is constant, or 
does not change rapidly in value. 

For convenience in computation, certain units of E. M. F., of elec- 
tric resistance and of electric current are employed. 

The Practical Unit of E. M. F. is called the Volt, after Alexander 
Volta, the inventor of the voltaic cell. The volt is about equal to the 
pressure produced by the common blue-stone cell, usually employed in 
telegraphy. 

The Practical Unit of Electric Resistance is called the Ohm, after Dr. 
Ohm. The ohm is, approximately, the resistance offered by two miles 
of ordinary copper trolley wire, or by one foot of No. 40, A. W. G. 
(American wire gauge) copper wire. 

The Practical Unit of Electric Current is called the Ampere y from Ampere, 
a French physicist. The ampere is such a rate of current as will pass 
through a circuit whose electric resistance is one ohm, under an E. M. F. 
of one volt. 

Ohm' s law is readily expressed as follows : 

^ E A Volts 

or Amperes 



K ' * Ohms 

In a hydraulic circuit, the current of liquid that passes in a given 
time, say in one second, is measured by the quantity of liquid per 
second, as for example, so many cubic feet per second. So in an elec- 
tric circuit, the electric current is measured as a given quantity of elec- 
tricity per second. 

The Unit of Electric Quantity is called the Coulomb, after the French 
physicist, Coulomb. An ampere is a current of one coulomb per second. 

401. Insulators. — Bare telegraph, telephone, and trolley 
wires are usually employed in those portions of their 
circuits that are outside of buildings. In such cases, it is 
necessary to support the conductors on insulators of glass 
or other non-conducting material. When the wires enter 
buildings they are insulated with coverings of rubber, jute, 
cotton or other material, either with or without a coating 
of some insulating wax or resin. A form of glass insula- 
tor is shown in Fig. 155. The screw-thread, in the interior 
of the insulator, is provided for its attachment to a wooden 
pin supported on the cross arm. 




ELECTROSTATICS. 265 

When the E. M. F. is great, as in the case of frictional electric ma- 
chines, it is necessary to insulate the conductors very carefully. Moist- 
ure deposited on the surface of insulators 
from damp air, is a partial conductor of 
electricity, while dry air, at ordinary pres- 
sures, is a non-conductor. All experiments 
with the electrical charges of high electro- 
motive forces produced by frictional machines 
should, therefore, be tried in dry, cold 
weather ; since in damp, warm weather, an 
electrified body rapidly loses its charge, owing 
to the condensation of moisture on the in- 
sulating supports. 

402. Electric Charge. -When Fig 7^^^ or . 
conducting wires, connected to any 

electric source, are not connected to each other, so that 
the circuit is broken or opened, although no continuous 
current will flow, yet the E. M. F. of the source will pro- 
duce what is called an electric charge. 

403. Electric Charge Produced by Friction. — If a 

dry rod of glass, or a stick of sealing-wax, be briskly 
rubbed with a piece of dry silk or flannel, it acquires the 
power of attracting or repelling light objects. The glass 
or w T ax has become electrified by means of the friction, 
and has acquired an electric charge. Generally, the E. M. 
F.'s produced by friction are much greater than those 
produced by either voltaic cells, or by dynamo-electric 
machines. 

404. Effects Produced by Electric Charges.— If a 

body possessing an electric charge, such as a rubber comb 
which has been briskly rubbed with a silk handkerchief, 
be brought near the face, a creeping sensation will be ex- 
perienced, as though cobwebs were touching it. If the 
electrified body be brought near a blunt metallic con- 
ductor, or a knuckle of the hand, the body will be dis- 
charged, and a faint bluish spark will pass to the metal or 

x 



266 



NATURAL PHILOSOPHY. 



to the hand, with a slight crackling sound. The faint light 
and feeble sound in this case are of the same character as 
the lightning flash and the thunder peal, which attend 
the discharge of a cloud to a neighboring cloud, or to the 
earth; in this latter case E. M. F.'s of probably millions 
of volts are acting. The science which treats of electric 
charges and their effects is called electrostatics. 

405. Electrostatic Attractions and Repulsions. — 

Attractions and repulsions between electrified or charged 
bodies may be conveniently shown by means of a pith-ball, 
suspended by a silk thread from any suitable support, as 
shown in Fig. 156. If a rod of glass, that has been rubbed 





Fig. 156.— Electrostatic Attractions and Repnlsions. 

with a dry silk handkerchief, is brought near the pith-ball, 
the latter is attracted to the glass, as shown at A. As soon 
as the pith-ball touches the glass rod, it is repelled from it, 
as shown at i?, and if not allowed to touch the ground, or 
any ground-connected conductor, will continue to be re- 
pelled. If, however, it touches such a body, it will again 
be attracted to the rod, and again repelled. 

If another electrified body, as a piece of sealing-wax 
rubbed with flannel, be brought near the pith-ball while 
it is quietly hanging from its support, it will be attracted 
and repelled as it was by the glass. If, however, while the 
pith-ball manifests repulsion for the electrified glass, the 



ELECTR OSTA TICS. 



267 



electrified sealing-wax be brought near it, it -is at once 
attracted ; or, if it be repelled by the wax, it is attracted by 
the glass. 

If any other substance be electrified by friction, we will 
ind that it acts either like the glass or like the wax ; we, 
therefore, conclude that there are but two kinds of elec- 
tric charge or excitement; viz., one like that excited in 
glass rubbed with silk, and one like that excited in wax 
rubbed w T ith flannel. The former is called a positive charge 
ind the latter a negative charge. Positive charges are gen- 
erally represented by + ; negative charges by — . 

The law of electrostatic attractions and repulsions may 
3e stated as follows : Similar charges repel; dissimilar charges 
ittract. 

When any body receives an electric charge by friction, both the 
body rubbed, and the body with which it is rubbed, receive an electric 
charge. Moreover, one of these bodies is charged positively and the 
other is charged negatively. 

406. Electroscope. — The character of any electric 
charge is determined by means of an instrument called 
in electroscope. The pith-ball, 
shown in Fig. 156, is a simple 
electroscope. A better form, 
lowever, consists of two small 
strips of gold leaf n, n, Fig. 
157, attached to a metal rod, 
terminating in a metal ball c. 
The gold leaves and rod are 
placed in a glass jar J?, inside 
of which the air can be kept 
free from moisture. If the 
ball be touched by an electri- 
fied body, the gold leaves re- 
ceive a charge of the same 
kind as that in the electrified body, and are, therefore, re- 
pelled. 




Fig, 157.— An Electroscope, 



268 



NATURAL PHILOSOPHY. 



To determine the character of any charge, by means of the electro- 
scope, the gold leaves are repelled by a known charge, say positive ; 
and, while the leaves are thus diverged, the charge of unknown charac- 
ter is brought near the ball c, and the movements of the gold-leaves 
carefully observed. If they are still further repelled, the charge of 
the body is positive ; if, however, the leaves approach each other, the 
charge is negative. 

Experiment 88.— Suspend A and B, two pieces of gold or silver 
paper, about two inches square, by pieces of sewing silk to a rod or 
other support as shown in Fig. 158, so that they shall 
be directly opposite each other. They will form an ex- 
cellent electroscope. If the leaves be touched by an 
electrified body, they will be repelled ; and, if the air 
be dry, will continue to stand apart for a long time. 

407. Positive and Negative Charge. 

— The kind of electricity produced by fric- 
tion, that is, whether positive or negative, 
depends on the bodies that are rubbed 
together. 

In the following list the different sub- 
stances are so arranged that each will be 
positively charged, if rubbed by any body 

which follows it, and negatively charged, if rubbed by any 

body which precedes it 

1. Cat's skin. 4. Cotton. 7. Wood. 

2. Woolen fabrics. 5. Silk. 8. Sealing-wax. 

3. Glass. 6. The hand. 9. Hard rubber. 
Thus, if glass be rubbed with flannel or cat's skin, it 

becomes negatively charged ; but, if rubbed with cotton or 
silk, it becomes positively charged. 

The rubber is always oppositely electrified to the thing 
rubbed. Glass rubbed with silk is positively electrified, 
while the silk is negatively electrified. 

408. Electrostatic Induction. — If an insulated con- 
ductor, such as the cylinder A B, Fig. 159, be brought 
near a positively charged body C, the cylinder will ac- 
quire a negative charge at the end A, nearest C, and 




Fig. 158 -A Sim- 
ple Electroscope. 



ELECTBOSTA TICS. 



269 



a positive charge, at the end j5, farthest from C. The 
pith-balls attached to the cylinder A B, will show that 
these charges are greatest at the extremity, and prac- 




A I 1 1 A A 



Fig, 159.— Electrostatic Induction. 

tically absent at the middle part. Induction produced 
in this way by an electric charge is called electrostatic 
induction. 

Electrostatic induction takes place through the air or other non-con- 
ducting medium between C, and A B. Any medium which thus per- 
mits electrostatic induction to take place through it is called a dielectric. 
All non-conductors or insulators are dielectrics. Electrostatic induction 
is due to a peculiar activity in the ether surrounding an electrically 
charged body, called electrostatic flux. 

409. Cause of the Attractions and Repulsions of 
Excited Bodies. — 

Alternate electric at- 
tractions and repul- 
sions are the results 
of electrostatic induc- 
tion. If an unelec- 
trified pith - ball i?, 
Fig. 160, be brought 
near a conductor A, 
charged with positive 
electricity, it is at once 
electrified by induc- 
tion. The side of the pith-ball nearer A, receiving an op- 
I posite charge to that of A, the ball is attracted to the con- 



/ 



C 



B 




Fig. 160.— Oanse of Electrical Attraction and 
Repnlsion. 



270 NATURAL PHILOSOPHY. 

ductor. As soon as the ball touches the conductor, it re- 
ceives a positive charge and is, therefore, repelled. If, now, 
it should touch a ground-connected body, as (7, it will be 
again attracted and repelled as before. 

410. Distribution of an Electric Charge. — All the 
electric charge on an insulated conductor lies on the out- 
side of the conductor. If an insulated hollow sphere, 
provided with a hole in the top, is charged with electricity, 
a small metallic disc attached to the end of a glass rod, if 
touched to the outside of the sphere at any point will take 
away a small charge of electricity, as may be proved by 
an electroscope. But if touched to any part of the inside 
of the sphere, it will be found to contain no electric charge, 
all the charge of the sphere residing on its surface. 

This is true only of an electric charge. When the electricity is in 
steady motion, as an electric current, then it passes through the whole 
substance of the conductor. 

411. The Influence of Points on an Electric 
Charge. — In a charged insulated sphere, the electric 
charge has the same value over all parts of the surface ; 
but if the excited conductor be egg-shaped, then the 
charge is greatest near the point of the egg, and this will 
be found to increase with the sharpness of the point, so that 
when the end is very sharp, the charge may become suffi- 
ciently powerful to enable the electricity to escape directly 
into the air. Conductors intended to retain an electric 
charge are, therefore, made blunt or rounded so as to 
prevent this loss of charge. 

412. Electric Machines. — The Electrophorus. — 
The simplest form of electric machine, the electrophorus, 
consists of a plate A, Figs. 161 and 162, of brass or other 
metal, attached to a glass rod, and a plate of resin B, 
placed in a metallic dish. The resin is negatively ex- 
cited by rubbing it briskly with a piece of cat-skin. The 
plate A, held by the glass handle, and placed over the 
resin, as shown in Fig. 161, becomes electrified by indue- 



ELECTROSTATICS. 



271 



tion, the side nearest the resin being positively charged, and 
the side farthest from it, negatively charged. If A, is now 
raised from the resin, without previously touching it to any 





Fig 161— Electrophorus (Charging). Fig, 162 — Electrophorus (Discharging), 

conductor, it will be found to possess no charge, since the 
electricity on the positive side of the disc flows toward the 
negative side, and neutralizes it. If, however, the disc be 
touched by the finger, as shown in Fig. 162, it will, when 
raised from the resin, possess a free positive charge. 

Experiment 89. — An electrophorus may bemadeas follows : Place 
in a tin pie-plate, in equal parts, rosin and gum-shellac, sufficient in quan- 
tity, when melted, to nearly fill the plate ; place the dish over a fire, and 
very gradually melt the rosin and shellac, at the same time stirring so as 
to break air-bubbles. When melted, set the dish on a flat support to 
cool. Now cut a disc of wood smaller in diameter than the rosin surface of 
the plate ; bore a hole in the middle of the wood and cement in it a glass 
rod or tube. Paste tin foil over the wooden disc, covering it completely, 
and remove any rough ends by smoothing the foil with the finger-nail. 
To operate, rub the rosin plate with a bit of silk or cat-skin, and place 
the tin-foil disc on the rosin, and touch it with the hand. On removing 
the disc a spark, or discharge of positive electricity, may be taken from 
it by the knuckle. When the rosin-plate has once been charged by rub- 
bing, an indefinite number of sparks may be obtained by placing the disc 
each time on the rosin, and touching with the finger, as before. When 
the air is cold and dry, as in winter, and the glass handle clean and dry, 
sparks of considerable length may be obtained. 

4-13. The Plate Electrical Machine. — This machine 
consists of a circular plate of glass A, Fig. 163, mounted 
on an axis B, on which it may be turned by means of an 



272 



NATURAL PHILOSOPHY. 



insulated handle C. At D, a rubber, of piano felting or 
chamois skin, is pressed by brass springs firmly against 
the plate. The rubber has generally an amalgam spread 




Fig, 163.— Plate Electrical Machine. 

over its surface, and is in electric contact with an insulated 
conductor J5, called the negative conductor. A series of 
metallic points F, connected with an insulated conductor 




Fig. 164— Tbpler-Holtz Machine. 

0, called the positive conductor, is placed near that part 
of the plate diametrically opposite the rubber, as shown. 



ELECTROSTATICS. 273 

On turning the handle, the friction of the rubber gives the 
glass a positive charge and the rubber a negative charge. 
The negative conductor is now charged by the rubber, 
while the electricity on the glass, coming opposite the 
points, charges the conductor connected with them posi- 
tively. The lower half of the plate is loosely covered by a 
bag of silk S. When only positive electricity is desired, a 
chain TF, connects the negative conductor with the ground. 
A more powerful form of machine, called an electrostatic 
induction machine, is shown in Fig. 164. This form is 
called the Topler-Holtz machine. It is practically a re- 
volving electrophorus. 

414. The Leyden Jar or Condenser. — In 1745, Von 
Kleist of Pomerania, while experimenting with a fric- 
tional electric machine, hung a small vial containing 
mercury, on one of the prime conductors of the machine. 
The vial was supported by a bent wire, passing through the 
cork of the bottle, and dipping down into the mercury. 
While attempting to remove the bottle he received what 
he considered a severe shock. He thus discovered what 
is now known as the Leyden jar or condenser. 

415. The Leyden Jar. — The Leyden jar usually 
takes the form shown in Fig. 165, where the lower part of 
a glass jar is coated on the inside and out- 
side with tin foil. The inside coating is 
in connection with the brass knob A, by 
means of the chain E. To charge the jar, 
it is held in the hand which grasps the 
outer coating, while the knob A, is brought 
near the conductor of an electrical machine, 
and a number of sparks passed into the 
jar. If now, one hand be placed on the Fig, 165 —The 
outer coating, and the other on the knob A, 

a discharge will pass through the body and give a more or 
less severe shock. 

18 




274 



NATURAL PHILOSOPHY. 



A battery of Leyden jars consists of a number of jars 
having their inner and outing coatings respectively con- 
nected with one another so as to act as a single large jar. 
The discharge from a Leyden jar may be passed through a 
number of persons joined hand to hand, the person at 
one end of the line touching the outside coating of the 
jar, and the person at the other end, the knob. The dis- 
charge from a very large battery may prove fatal. 

416. The Condenser. — In practice, the condenser, 
which differs from the Leyden jar only in shape, usually 
takes the form of a pile or bundle of metallic plates, 
separated by thin sheets of mica, oiled silk, or paraffine 
paper. A form of condenser is shown in Fig. 166. The 




Fig, 166.— A Condenser, 

capacity of such a condenser increases with the area of 
the metallic plates, and the thinness of the insulating 
sheets. In order to discharge a condenser, it is necessary 
to connect the opposite terminal coatings by some con- 
ductor. The discharge occurs as a bright flash accom- 
panied by a loud detonation. It can be shown that such 
a discharge does not consist of one single discharge, but of 
a number of separate discharges that are alternately oppo- 



ELECTROSTATICS. 275 

sitely directed. In other words, the discharge of a con- 
denser is rapidly alternating or oscillatory. 

417. Atmospheric Electricity.— The atmosphere usu- 
ally contains a positive charge, though it sometimes 
changes rapidly to negative on the approach of clouds, 
or in stormy weather. The charge is least near the earth's 
surface, and increases with the altitude. 

418. Lightning. — When the electric charge on the 
surface of the drops of moisture in a ckmd has reached a 
sufficient E. M. F., a lightning flash may occur. When 
such a cloud comes near the earth, the ground below it 
becomes oppositely charged by induction ; and when these 
opposite charges acquire sufficient E. M. F., they discharge 
into each other through the air, the flash which accom- 
panies the discharge being called lightning. An electrified 
cloud sometimes discharges into a neighboring cloud which 
is oppositely charged. The lightning discharge which is 
accompanied by a loud peal of thunder is an oscillatory 
discharge. The discharge from the cloud may, however, 
be steady. In this case there is no accompanying thunder. 

The thunder which follows the lightning is caused by 
the violent disturbance in the air produced by the vacuum, 
formed by the rapid formation and condensation of vapor 
on the passage of electricity through drops of rain. 

419. Lightning Rods consist of stout rods of iron or 
copper, attached to the outside of the building to be pro- 
tected, and extending some little distance above its high- 
est point. The upper end of the rod should be pointed, 
and its lower end should extend deep into the ground, 
until it reaches permanently damp earth, or some other 
good conductor of electricity. If underground water- or 
gas-pipes are in the neighborhood, it is well to connect 
the rod to them. If the roof of the building be of metal, 
such as tin or copper, it should be connected with the 



276 NATURAL PHILOSOPHY. 

rod. The rod should be of sufficient thickness to con- 
duct to the earth, without being melted, the heaviest dis- 
charge that may strike the building. For all oscillatory 
discharges, a stranded conductor; i.e., a conductor com- 
posed of separate conductors, is better than a single con- 
ductor. A lightning-rod, not well electrically connected 
with the earth, is a source of danger rather than of pro- 
tection. 

420. Experiments in Frictional Electricity. —A 

number of instructive electrical experiments may be 
shown with easily contrived apparatus. The student is 
earnestly advised to make the information his own, as far 
as possible, by verifying facts by experiment. 

Experiment 90. — Cut a piece of elder pith into a ball; tie it to a piece 
of silk, and suspend it from any support. Try the effect of rubbing 
different bodies together, and holding them near the pith-ball, to see 
whether they are electrified. 

Experiment 91 . — Cut two strips of gilt paper, a and b, about one inch 
long, and connect them, as shown in Experiment 88, but with linen or cot- 
ton thread instead of silk. Stick a wire through a cork of a wide-mouthed 
bottle, and tie the threads to the end of the wire, leaving 
the discs hanging by about i inch of thread. Solder 
a smooth metal button A, to the end of the wire, and 
put the cork in the bottle, so that the pieces of paper 
shall be inside the bottle, as shown in Fig. 167, first, 
however, being sure that the bottle is perfectly dry by 
heating it on a warm stove. The cork also must be 
perfectly dry. Eun melted sealing-wax over the top 
Fig. 167.— An 0I * ^ ne cor k, so as to prevent any moist air from after- 
Electroscope, wards getting into the bottle. This apparatus will now 
serve as an electroscope. 

Experiment 92.— Attach a long metallic wire to the button A, of the 
electroscope just made. Excite the electrophorus described in Experiment 
89, and touch the far end of the wire with the tin-foil disc. The leaves a 
and b, will at once diverge, showing that the wire has conducted the elec- 
tricity to them. Try the same with a dry silk thread, and prove that it 
is a poor conductor. 

Experiment 93. — In the corners of a square piece of wood, bore 
four holes, large enough to insert the necks of four beer bottles. 





ELECTROSTATICS. 277 

Stand a person on this insulating stool, and charge him with electricity 
from the electrophorus by giving him 15 or 20 sparks from the tin-foil 
disc. If, now, the knuckle be approached to any part of his body, an 
electric spark will pass from it to the knuckle. While on the stool he 
can light the gas with the spark from his finger. 

Experiment 94.— Place a person on the insulating stool, and let him 
hold the electroscope. Fig. 167, in his hand, with his finger on the knob A. 
Then strike him on the back with a piece of cat-skin ; at every stroke the 
leaves a and 6, will be seen to diverge. 

Experiment 95.— Suspend by silk threads a and b, as shown in Fig. 
168, a tomato can, free from sharp edges ; attach to the 
lower side, by linen or cotton thread, pith-balls c and d, 
and you have an insulated conductor. 

Experiment 96.— Make another such conductor, 
and try the effects of induction as described in £ 408. 

Experiment 97.— Procure a sheet of letter paper, 
and a smooth pine board, somewhat larger than the paper. 
Heat the board and paper before a fire. Then place the pig, 153, 

paper on the board, and stroke it briskly with a piece of An Insulated 
India-rubber, such as is used for erasing lead-pencil Conductor, 

marks. The paper will become strongly electrified. 
Now lift the paper from the board by one of its edges, and bring it near 
the wall, and it will be at once attracted to the wall, and will cling to it 
for several minutes. 

Experiment 98. — Electrify the paper as before, and while it is on 
the board, cut it into strips. Take hold of all the strips at one end, and lift 
them from the board. Their lower ends will be repelled, and will stand 
out from one another in an amusing manner. 

Experiment 99. — Electrify a piece of paper as before. Eemove it 
from the board, and lay a pith-ball on it. The ball will either be thrown 
off the paper at once, or it will run to the lower side of the paper, and will 
then be shot off from it. 

Experiment IOO. — Place a metal waiter on top of a dry glass goblet. 
Electrify the paper and place it on the waiter. Apply the knuckle of 
the hand to the edge of the waiter, and a spark will pass to it. Eemove 
the paper by the edge, and another spark can be taken from the paper. 

Experiment IOI. — Support a piece of window-glass, about an inch 
above the surface of a table. Place a few pith-balls under the glass, and 
rub the top of the glass briskly with a piece of silk or cat-skin. The balls 
will move about in a curious manner, and some will, probably, stick to the 
glass. Stop rubbing, and hold a finger near the glass above the balls, 
and they will at once fall. 

y 




CHAPTER XXIII. 

MAGNETISM. 

«K>X^OC 



421. Magnetism. — A magnetic needle; i. e., a magne- 
tized bar of hardened steel, shaped and supported as 
shown in Fig. 169, when free from the influence of sur- 
rounding bodies, will 
come to rest with its 
end N, pointing, ap- 
proximately to the 
earth's north geo- 
graphical pole. If 
another bar of mag- 
netized steel be held 
with its end iV, near 
the end N } of the 
needle, but without 
touching it, the needle 
will be deflected and 
will come to rest with its end £, pointing to the end N 9 
of the bar. These movements are due to what is called 
the magnetism of the needle and bar. 

Magnetism apparently possesses the power of acting at 
a distance across an empty space. This, however, is not 
the case, because, as we have already seen, space is filled 
with ether, and the properties of magnetized bodies are 

278 




Fig. 169.— A Magnetic Needle. 



MAGNETISM. 279 

due to magnetic flux, a peculiar condition of activity in 
the ether surrounding the magnet. 

422. Magnetic Poles. — If either the magnetic needle 
or the magnetized bar be rolled in iron filings, the filings 
will adhere to the neeedle or bar, collecting near the ends. 
These points or places are called magnetic poles. If a 
magnet be supported as in Fig. 169, so as to turn freely, 
that end which comes to rest pointing, approximately, to 
the earth's geographical north pole, is called the positive 
or north-seeking pole; and that end which comes to rest 
pointing, approximately, to the earth's south pole, is called 
the negative, or south-seeking pole. The positive pole is usu- 
ally indicated by the sign +, or the letter iV, and the nega- 
tive pole by the sign — , or the letter S. 

423. Magnetic Flux Paths. — Though magnetic flux is 
invisible, yet its paths may, in many cases, be readily 



, ,v v - - -—J 




mmiiMmmm^S^ 



Xl~ 



Fig, 170.— Magnetic Flux Paths over Pole of Vertical Bar Magnet. 

mapped out by means of the action which the flux exerts 
on small particles of iron. If a plate of glass, or a sheet 
of stiff paper, be held horizontally over a magnet pole, 
and fine iron filings be sprinkled over the plate or sheet, 



280 



NATURAL PHILOSOPHY. 



the filings will arrange themselves along the general direc- 
tions of the flux paths, when the plate or sheet is gently 
tapped. 

Fig. 170, shows the manner in which iron filings have 
distributed themselves on a sheet supported over one pole 
of a vertical bar magnet. This figure was obtained by 
holding the magnet vertically under a horizontal plate. 
The arrangement of the magnetic flux, or streamings 
around the end of the magnet, is clearly shown. 

Experiment 102. — Place a bar magnet on a table, and lay over it a 
piece of smooth window glass, or a sheet of stiff paper stretched in a 
frame. Sprinkle some fine iron filings on the glass or paper, tap the 
edge gently with the finger, and the filings will be arranged in curved 
paths, which are the paths in which the magnetic flux flows, as shown 
in Fig. 171. 




Fig. 171.— Magnetic Flux Paths over Horizontal Bar Magnet. 

424. The Magnetic Circuit. — The magnetic flux 
comes out of a magnet at one point or place, passes through 
the air or other medium surrounding the magnet, and re- 
enters the magnet at some other point or place. These 
points or places are called the poles of the magnet, and 
the completed path or circuit through which the flux 
passes, is called the magnetic circuit. We do not know 
from which pole the flux emerges, or at which it re-enters 
the magnet; but, for convenience, it is assumed that the 



MAGNETISM. 281 

flux issues from a magnet at its north-seeking pole and 
re-enters it at its south-seeking pole. 

425. Magneto-Motive Force. — In the case of an elec- 
tric source, the force which produces the electric flux or 
current is called the electro-motive force ; or, as it is usually 
contracted, E. M. F. In the case of any magnet, the force 
producing the magnetic flux or current is called the mag- 
neto-motive force, usually contracted, M. M. F. 

The resistance which any circuit offers to the passage 
of magnetic flux is called its magnetic resistance or reluc- 
tance. The reluctance of air, copper, wood, glass, etc., is 
very nearly the same. The reluctance of iron and steel is 
enormously lower than that of air. 

426. Natural Magnets. — There exists an ore of iron 
called magnetic oxide, specimens of which are sometimes 
found possessing the properties of magnets. Such mag- 
nets are called lodestones, or natural magnets, to distinguish 
them from those made artificially. 

427. Magnetic Attractions and Repulsions. — If the 
north-seeking pole of a magnet be brought near the south- 
seeking pole of a magnetic needle, they attract each other ; 
if the north-seeking pole be brought near the north-seeking 
pole of the needle, they repel each other. In other words, 
like magnetic 'poles repel, and unlike magnetic poles attract; 
that is, north attracts south, and south attracts north ; but 
north repels north, and south repels south. 

The region surrounding a magnet, and pervaded by its 
magnetic flux, is called a magnetic field. 

428. Theory of Magnetism. — Although the exact 
nature of magnetism is unknown, yet magnetism is gen- 
erally believed to be a property inherent in the ultimate 
particles of matter. In other words, the molecules, or 
possibly the atoms, are believed to be naturally magnetic, 
each giving out magnetic flux from one point or pole, and 
taking it in again at another point or pole. According to 



282 NATURAL PHILOSOPHY. 

this conception it would be impossible to have a magnet 
with one pole only, since, where the flux passes out of the 
atom is its N-seeking pole, and where it enters it, is its S" 
seeking pole. 

Examining the groupings of iron filings on a bar mag- 
net rolled in iron filings, it might appear that one entire 
half of the bar possessed north polarity only, and the other 
half possessed south polarity, and that, therefore, if the 
bar were divided at its central part, we should have one 
magnet all of north polarity only, and another all of 
south polarity. If, however, this experiment be tried, it 
will be found that the cut ends possess poles of nearly 
the same strength as the former free ends of the bar. 
And this will be the case no matter how often the bar 
be divided. 

Experiment 103. — Magnetize apiece of watch-spring by stroking 
it with a magnet. Eoll the spring in iron filings and observe that they 
collect at the ends only. Cut the spring at its middle point by a pair 
of shears, and observe, on rolling the pieces in filings, that they collect 
equally at the free ends. Continue bisecting the pieces, and observe that 
in every case, poles are established at the ends, and that the central parts 
collect no filings. 

429. Magnetization. — When a magnetic substance, 
such as iron, is brought into a magnetic field, and is 
traversed by magnetic flux, it thereby becomes magnet- 
ized. While unmagnetized, the molecular magnets have 
no definite direction, but point in all directions. The act 
of magnetization is believed to consist in so directing the 
molecular magnets that they are all turned in the same 
general direction. When all the molecular magnets are 
turned in the same direction, the body acquires its greatest 
magnetization, or reaches magnetic saturation. 

Magnetic substances differ in the ease with which the 
molecular magnets are thus similarly directed ; i. &, in the 
ease with which they are magnetized. Some substances, 
like soft iron, are readily magnetized ; others, like steel, 
nickel, manganese and cobalt, are more difficult to mag- 



MAGNETISM. 283 

netize, while all other substances can scarcely be magnet- 
ized at all. 

Soft iron loses nearly all of its magnetism almost im- 
mediately after the magnetizing force has been removed. 
Hard steel, on the contrary, retains nearly all of its mag- 
netism after the removal of the magnetizing force. Soft 
iron, therefore, acquires a temporary magnetism only ; hard- 
ened steel, a permanent magnetism. 

430. Magnetic Induction. — A bar of steel, or other 
magnetizable body, may be magnetized either by rubbing 
it with or against a magnet, or by merely bringing it into 
the flux of a magnetic field. In either case it becomes 
magnetized by having its molecular magnets brought into 
alignment by the magnetizing flux. This latter process is 
called magnetic induction. In all cases the induced polarity 
is. of the opposite name to that of the inducing polarity. 
The reason is simple. The magnetic streams are so directed 
as to take the same 
path as that of the 
magnetizing flux. If, 
as in Fig. 172, a bar 

1 m o Fig, 172.— Magnetic Induction, 

into the neighborhood 

of the north-seeking pole iV, of a magnet NS, the flux 

streams from the magnet will enter at the near end £', 

thus giving it a south-seeking pole, and will emerge at 

the far end A 77 , thus giving it a north-seeking pole. 

Experiment 104. — Touch one end of a steel pen to the north pole of 
a magnet. Throw the pen in some iron filings, and it will be found to have 
a pole both at the end touched and at the opposke end. Test the polarity of the 
end touched, by means of a magnetic needle, and it will be found to be 
south, and that of the opposite end of north polarity. 

Experiment 105. — Move one end of a steel pen several times very 
near the north pole of a magnet, without actually touching it. Iron 
filings will show poles at each end, and a magnetic needle will show r that 
the end w^hieh was brought near the north pole of the magnet has ac- 
quired south polarity, and the opposite end north. 




284 NATURAL PHILOSOPHY. 

431. Cause of the Magnetic Needle Pointing to- 
wards the Earth's North Geographical Pole. — A 

magnetic needle points to the north geographical pole of 
the earth for the same reason that the opposite poles of 
magnets point to each other, when they are sufficiently- 
near and free to move. The earth acts as a huge magnet, 
with its magnetic poles in the neighborhood of the geo- 
graphical poles of the earth, and the magnetic needle points 
towards these poles on account of their attraction. 

Since it is the opposite poles of magnets that attract 
each other, that end of the needle which points towards 
the north-magnetic pole of the earth must be of the oppo- 
site polarity to the earth's polarity at the north. 

432. Cause of the Earth's Magnetism. — The exact 
cause of the earth's magnetism is not known. We may 
regard the earth as a huge magnet with streams of mag- 
netic flux entering its mass in the neighborhood of the 
north geographical pole, and leaving it again in the neigh- 
borhood of its south geographical pole. These flux streams, 
though usually maintaining the same paths or directions 
and the same strength or density, vary slightly both in 
direction and intensity during different hours of the day, 
during different times of the year, and during different 
cycles of time. When a magnetic needle is brought into 
the earth's magnetic flux, it will, if free to move, come to 
rest when threaded by the flux of the field in the same 
direction as that in which its own flux passes through it. 
Magnetic needles, therefore, placed in the earth's field will 
show by their direction when at rest, the direction of the 
earth's flux, and may, therefore, be employed to detect the 
variations which occur in the direction of the earth's flux. 

433. Variations in the Earth's Magnetism. — Varia- 
tions in the intensity and direction of the earth's magnet- 
ism may be divided into four classes ; viz., 

1. Diurnal variations, or those which occur at different 
hours of the day. 



MAGNETISM. 



285 



2. Annual variations, or those which occur at different 
seasons of the year. 

3. Secular variations, or those which occur at different 
cycles or long intervals of time. 

4. Irregular variations, or those which attend either out- 
bursts of solar activity called sun-spots, or unusual elec- 
tric manifestations on the earth, called magnetic or electric 
storms. 

434. The Declination or Variation of the Needle. 

— It is a common though mistaken notion, to suppose that 
the magnetic needle invariably points to the true geo- 
graphical north. The fact is, that except in a few locali- 
ties, the needle actually points to the east or west of the true 
north. This deviation of the needle from the true north, 
is called the declination, and in some localities the amount 
of this declination is considerable. 

435. The Inclination or Dip of the Needle.— The 

earth's magnetic flux does not 
in most places flow parallel 
to its general surface. There- 
fore, w 7 hen a magnetic needle is 
free to move in a vertical as 
well as in a horizontal direc- 
tion, it retains its horizontal 
position in but few parts of the 
earth. In most places, one of 
the poles inclines or dips to- 
wards the earth. This is called 
the dip or inclination of the 
needle. In the Northern hemi- 
sphere, it is the north-seeking pole, and in the Southern 
hemisphere, the south-seeking pole that dips or inclines 
towards the earth. The magnetic dip or inclination at 
any point is determined by means of what is called a 
dipping circle, as is seen in Fig. 173. 




Fig. 173 —Dipping Circle. 




5SF*» 



CHAPTER XXIV. 

ELECTRIC CURRENT.— ELECTRO-MAGNETISM. 



«*>>©<o 



436. Electric Sources. — Although the values of the 
E. M. F.'s produced by friction are very high, amounting 
usually to thousands, or hundreds of thousands of volts, 
yet the resistances in their circuits are also so high, that 
the current strength produced is usually but a small frac- 
tion of an ampere. To produce powerful currents, it is 
necessary to employ electric sources whose resistance is 
low. A variety of such sources exist; the most import- 
ant are the voltaic cell, the thermo-electric cell, and the 
dynamo-electric machine. 

437. Varieties of Electro-Motive Force. — The E. 

M. F.'s produced by electric sources are of a variety of 
types. The most important of these are the direct or con- 
tinuous E. M. F, and the alternating E. M. F. A direct or 
continuous E. M. F. is one which always has the same 
direction. An alternating E. M. F. is one which period- 
ically alternates or changes its direction. 

When these E. M. F.'s act on closed electric circuits 
they respectively produce either direct or continuous electric 
currents; i. e., those which continue to flow in the same 
direction; or alternating electric currents ; i. e., those which 
periodically change their direction. Voltaic or thermo- 

.286 



ELECTRIC CURRENT.— ELECTRO-MAGNETISM. 287 

electric cells produce direct E. M. F.'s and currents. The 
ordinary dynamo-electric machines produce alternating 
E. M. F.'s and currents, unless provided with devices 
called commutators, in which case they produce direct E. 
M. F.'s and currents. 

438. Voltaic Cells. — When any two dissimilar metals 
are dipped into a liquid that is capable of acting on one 
of them, an E. M. F. is produced whose value depends on 
the nature of the metals and on the nature of the liquid 
into which they are dipped. Any two substances that 
are used together for this purpose form what is called a 
voltaic couple; the exciting liquid is called the electrolyte; 
and the entire arrangement a voltaic cell. As a rule, 
couples of carbon and zinc dipped in certain acid elec- 
trolytes, produce the highest E. M. F.'s. 

439. Galvani and Volta. — The production of E. M. 
F.'s by chemical action was first noticed by Galvani, an 
Italian physiologist, who erroneously ascribed the effects 
produced to the presence of a vital fluid. He was making 
experiments in which he used the legs of recently killed 
frogs. Hanging them against an iron balustrade, he no- 
ticed that whenever the metal touched a large nerve in 
the frog's leg, and so brought it into electric connection 
with the muscles of the leg, the legs violently twitched 
as in life. He thought that these movements were caused 
by a vital fluid which came out of the nerve, and flowed 
through the iron to the muscles. 

Volta, a distinguished physicist, showed that these 
movements were due to electricity and constructed an 
arrangement called a voltaic pile or battery, by means of 
which powerful continuous currents of electricity could 
be readily produced. This source was named the voltaic 
pile after his name. It is sometimes called the galvanic 
pile, though improperly, since this might imply a belief 
in Galvani's idea of the existence of a vital fluid. 



288 



NATURAL PHILOSOPHY. 



440. A Simple Voltaic Cell. — A simple voltaic cell 
consists of two plates of different metals immersed in a 
liquid which can readily act on one of them. One of the 
simplest forms given to the voltaic cell is seen in Fig. 174, 
where a plate of zinc and a plate of 
carbon are immersed in water contain- 
ing sulphuric acid. 

If the zinc be pure, as long as the 
circuit of the cell remains open, no ac- 
tion between the liquid and either 
plate occurs. On closing the circuit, 
however, an action takes place between 
the liquid and the zinc, and hydrogen 
gas, produced by the decomposition of 
the water, is seen to escape in minute 
bubbles from the carbon, and a current 
of electricity continues to flow in the direction indicated 
by the arrows as long as any chemical action continues. 

In the form of cell shown, the positive pole or terminal 
is the end of the carbon plate that projects out of the elec- 
trolyte, and the negative pole or terminal is the correspond- 
ing end of the zinc plate. 

Ordinary zinc is impure and is acted on by the electrolyte when the 
circuit is broken. This both wastes the zinc and liquid and weakens 
the strength of the current when the circuit is completed. It may be 
remedied by amalgamating the zinc ; i. e., by dipping it in acid water, 
and then rubbing some mercury over its surface. 




Fig, 174.— A Simple 
Voltaic Cell. 



441. Varieties of Voltaic Cells.— There is a great 
variety of voltaic cells, but they may all be arranged 
in two classes : 

1. Single-fluid cells, in which but a single electrolyte is 
employed. 

2. Double -fluid cells, in which two different electro- 
lytes are employed, one for each element of the voltaic 
couple. 



ELECTRIC CURRENT.— ELECTRO-MAGNETISM. 289 



Among the more important voltaic cells in common use 
are the Bichromate, the Gravity and the Leclanche. 

442. The Bichromate Cell consists of a zinc-carbon couple im- 
mersed in an electrolyte formed by dissolving potassium bichromate in 
water containing sulphuric acid. The liquid is at first of a bright red 
color, but on being used, soon changes to a greenish brown. This cell 
gives an E. M. F. of nearly two volts. The bichromate cell gives a 
fairly strong current when first connected to a circuit. In a compara- 
tively short time the current strength decreases, owing to what is called 
the polarization of the cell. Polarization is due to the formation of bub- 
bles of hydrogen on the negative plate. 

This polarization is best avoided by 
surrounding the negative plate by a 
separate electrolyte, capable of com- 
bining with the hydrogen as fast as 
it tends to be evolved. 

443. The Bunsen Cell consists of 
plates of zinc and carbon immersed in 
a solution of sulphuric acid in water 
and in strong nitric acid respectively. 
The nitric acid is contained in a por- 
ous cell. The zinc is in the form of a 
cylinder, and dips in the sulphuric 
acid in an outer cell. This cell pro- 
duces an E. M. F. of nearly two 
volts. 




Fig* 175.-The Nitric Acid Bat- 
tery, 



444. The Bluestone Gravity Cell.— In the early form of double- 
fluid cells, one of the electrolytes was kept in a porous cell of unglazed 
earthenware. The use of the porous cell was, however, found greatly 
to increase the resistance of the cell. The liquids in double-fluid cells 
are sometimes kept from mixing by their difference in density ; or, 
instead of using a depolarizing liquid around the negative plate, it is 
replaced by some solid depolarizing substance. The bluestone gravity 
cell is of the former type. It consists, as shown in Fig. 176, of plates 
of zinc and copper immersed respectively in solutions of zinc sulphate 
and copper sulphate. The zinc is hung near the top of the cell, and 
the copper plate is placed in the bottom of the cell, and surrounded by 
crystals of copper sulphate. The wire attached to the copper plate 
is insulated by wax or India-rubber. A saturated solution of copper 
sulphate half fills the jar, and on it floats the lighter solution of zinc 
sulphate. This cell produces an E. M. F, of about one volt. 
19 Z 



290 



NATURAL PHILOSOPHY. 



445. The Leclanche Cell consists of a zinc-carbon couple immersed 
in a solution of sal-ammoniac in water. The carbon plate is surrounded 
by a mixture of crushed carbon and black oxide of manganese. This 
cell is shown in Fig. 153. It gives an E. M. F. of about one and a half 
volts. It is very extensively employed for open-circuit work ; i. e., for 
work in which the cell is for most of the time on open circuit, being 
only employed to furnish current occasionally, as in the ringing of elec- 
tric bells. When kept on closed circuit it rapidly polarizes, but if polar- 
ized it will depolarize on open circuit. 

446. Voltaic Batteries. — When either the current or 
the E. M. F. required exceeds that given by a single vol- 




Fig. 176.— Voltaic Battery. 



taic cell, a number of cells are so connected as to act as a 
single cell, or as it is then called, a battery. 

In a series-connected battery ; i. e. , when the current passes successively 
through each of the cells of the battery, the E. M. F. of the battery is 
equal to the sum of the separate E. M. F.'s in the separate cells. A 
series-connected battery of two gravity cells is shown in Fig. 176. 

447. Thermo-Electric Couples. — If two bars of un- 
like metals, such as copper and iron, or antimony and 
bismuth, be soldered together at one end, the other ends 
connected by a conductor, and the soldered end heated, 
an E. M. F. will be produced and a current of electricity 
will flow in a certain direction through the circuit so pro- 
vided. If the soldered end be cooled, a current of elec- 
tricity will also be produced, but in the opposite direction. 



ELECTRIC CURRENT.— ELECTRO-MAGNETISM. 291 

Such an arrangement is called a thermo-electric couple or 
cell. A number of thermo-electric couples so connected as 
to act as a single electric source is called a thermo-pile or 
battery. A thermo-pile is shown in Fig. 177, where the 



A + 





Fig, 177 .— Thermo-Electric Pile or Battery, 

arrangement of each column of couples is shown on the 
right. If one face only of the pile is heated, an E. M. F. 
will be produced. 

Currents of electricity produced in this way by the action of heat, 
will continue to flow as long as there is any difference of temperature 
between the opposite ends of the bars, 

Thermo-electric E. M. F.'s are usually very feeble. They vary with 
the kind of metals used, and within certain limits, with the difference 
of temperature between the opposite ends of the couples. 

448. Electro-Magnetism. — Whatever may be the na- 
ture of electricity and magnetism, they are undoubtedly 
allied phenomena ; for, an electric current can never flow 
through a conductor without producing magnetic flux or 
magnetism ; and magnetic flux never cuts or crosses an 
electric conductor, or enters or emerges from a loop of a 
conductor, without setting up E. M. F.'s in such con- 
ductor. 

449. Magnetic Flux Surrounding an Active Con- 
ductor. — The passage of an electric current through any 
conductor, no matter what may be the material of which 



292 



NATURAL PHILOSOPHY. 




it is composed, is invariably attended by the production 
of magnetic flux in the space surrounding the conductor. 
This flux flows around the conductor in concentric cir- 
cular paths. Its direction depends on the direction of the 
current through the conductor, and, therefore, changes its 
direction when the direction of the current changes. 

The distribution of the flux surrounding an active con- 
ductor shown in Fig. 178, is obtained by passing the con- 
ductor through the centre of a 
sheet of stiff paper and sprink- 
ling iron filings on the same. An 
examination of the figure will 
show that the flux -paths sur- 
round the conductor in concen- 
tric circles whose planes are at 
right angles to the conductor. 

Fig, 178 —Magnetic Flux Sur- 
rounding Active Conductor. 450. Electro-Magnets. — If an 

active conductor be bent in the 

form of a circle or loop, its magnetic flux will enter 

the loop at one face and emerge from it at the opposite 

face. If the active conductor be bent in the form of a 

hollow coil or helix, its flux will also enter the coil at 

one face and leave it at the opposite face. 

In either case a change in the direction of the current 
through the conductor, will result in a change in the faces 
at which the flux enters and leaves the loop or loops. 

We have seen that in all magnets the flux emerges at 
one pole and returns to the magnet at the other pole, after 
passing through the circuit outside the magnet. Conse- 
quently, a single loop of active conductor, or a number 
of loops of such conductor, acts as a magnet and has a 
north-seeking pole at the end at which the flux emerges, 
and a south-seeking pole at the end at which the flux 
enters. A magnet produced in this way by an electric 
current is called an electro-magnet The strength of an 



ELECTRIC CURRENT.— ELECTRO-MAGNETISM. 293 

electro-magnet, like that of any other magnet, depends on 
the quantity of magnetic flux passing through the magnet. 
The quantity of flux produced by any single conducting 
turn or loop, depends on the current strength passing 
through that loop. If we increase the current strength, 
we increase the quantity of magnetic flux. If we increase 
the number of loops, the current strength remaining the 
same, we increase the quantity of magnetic flux, and, con- 
sequently, the strength of the magnet. To increase the 
strength of an electro-magnet we must, therefore, either in- 
crease the current strength or the number of turns or loops. 

451. Soft-Iron Cores of Electro-Magnets. — If a 
core of soft iron be introduced into a hollow coil or helix, 
the strength of the magnetic flux produced will be very 
greatly increased. Consequently, in all electro-magnets 
a core of soft iron is employed. The flux thus added to 
the magnet from the iron core is usually greatly in excess 
of that produced independently from the magnetizing cur- 
rents. 

452. Form of Electro-Magnets. — If a bar of soft 
iron N £, be wrapped with a few turns of insulated wire 
and connected to a voltaic cell, as shown in Fig. 179, the 




Fig. 179.— An Electro-Magnet. 



flowing of the current in the direction indicated by the 
arrows will produce a N-seeking pole at N y and a S-seek- 
ing pole at S. 



294 



NATURAL PHILOSOPHY. 



Electro-magnets are usually made of the horseshoe 
type, either by bending the bar or core at its middle point, 
or by winding separate magnetizing coils on separate cores 
and connecting them by a yoke of soft iron, as shown in 

Fig. 180. Usually a num- 
ber of layers of insulated 
wire are employed as shown 
in the figure. 

453. Uses of Electro- 
Magnets. — An electro-mag- 
net, when provided with a 
soft -iron core, possesses the 
valuable property of almost 
instantly acquiring and losing 
its magnetism when the mag- 
netizing current is established or interrupted. Electro- 
magnets are extensively employed in a great variety of 
apparatus, such as in dynamo-electric machines, electric 
motors, and in telegraphic, telephonic and signaling appa- 
ratus generally. 




Fig. 180.— Magnetism by Electro- 
Magnets. 




CHAPTER XXV. 

EFFECTS OF AN ELECTRIC CURRENT. 

~>XKo<> 

454. Effects Produced by an Electric Current. — 

The passage of an electric current through a conductor 
produces various effects, the principal of which are as 
follows : 

1. Thermal Effects. — The conductor becomes heated. 

2. Luminous Effects. — If the conductor be broken at any 
point a brilliant flash of light appears, provided the cur- 
rent passing be fairly great. When the current passing 
through any conducting wire is sufficiently strong, the 
wire is rendered incandescent, and emits light as well as 
heat. When discharges from an influence machine are 
passed through partially exhausted spaces, luminous ef- 
fects are produced. 

3. Mechanical Effects. — The passage of a powerful dis- 
charge through a conductor is often attended by its frac- 
ture or tearing, especially if its electric resistance be great. 

4. Physiological Effects. — Involuntary movements of the 
muscles of an animal are produced by an electric current 
sent through its body, not only during life, but also for 
some time after death. 

5. Chemical Effects. — An electric current sent through a 
liquid causes a decomposition of the liquid. 

6. Magnetic Effects. — All conductors conveying electric 

295 



296 NATURAL PHILOSOPHY. 

currents produce magnetic flux and, therefore, acquire the 
properties of magnets. 

455. Thermal Effects. — When an electric current 
flows through a conductor, it heats the conductor. In the 
case of a wire, unless the current be very great, the elevation 
of temperature is almost inappreciable provided the wire 
be stout and of good conducting material. If, however, 
the wire be of small diameter, so as to offer a high resist- 
ance in a short length, it may become intensely heated or 
even melted and vaporized by the current. The tempera- 
ture attained by the wire depends not only on the heat 
developed, but also on the surface of the wire through 
which this heat has to escape. The greater the amount 
of heat which has to escape from each square inch of sur- 
face in a given time, the higher the temperature the wire 
will attain. 

The amount of heat developed depends on the activity of the current, 
or the rate at which the electrical energy is expended. The practical 
unit of electric activity is called the watt. The watt is equal to the ac- 
tivity exerted by one ampere passing through a circuit under the pres- 
sure of one volt. The watt is, therefore, frequently called the volt- 
ampere. The watt is of a similar nature to the foot-pound-per-second, 
as employed in rating the activity expended by a stream of water es- 
caping from a reservoir, in which case the activity is equal to the quan- 
tity of water in pounds passing per second, multiplied by the distance 
through which it passes, in feet. So in the case of electric activity, 
the watt or the volt-ampere, is the flow of electricity in coulombs-per- 
second, multiplied by the electric level through which it falls in volts. 
One watt, or one volt-ampere, is equal to about 0.738 foot-pounds per 
second, or about y \q horse power ; or, in other words, 746 watts equal 
one horse power. 

456. Electric Heaters. — The heat produced by an 
electric current passing through a short conducting path 
of comparatively high resistance is utilized in the electric 
heater, in electric ranges or stoves, and in electric furnaces. 
One of the best examples of electric heaters is seen in the 



EFFECTS OF AN ELECTRIC CURRENT. 297 

heaters employed in some electric trolley cars. Here, long 
coils of wire, placed in convenient situations in the car, 
serve, when traversed by the current, to heat the cars. 

457. Luminous Effects. — The luminous effects of elec- 
tric currents are employed in a variety of ways. The 
principal of these are in arc and incandescent lighting. 
When a conductor conveying the current from a battery 
or dynamo is broken at any point, a brilliant flash of light 
is seen. If the ends of the wire connected with two pen- 
cils of carbon, are brought together, and then slowly sepa- 
rated, a brilliant arc or light, called the voltaic arc, will 
continue to pass between the electrodes, unless they be 
too widely separated. The light of the voltaic arc is of 
dazzling brightness, and the arc itself is the most intense 
source of heat that can be produced artificially. 

While the carbon electrodes are separated from each other, portions 
of the positive electrode, volatilized by the intense heat, are carried, 
in the form of an arc or bow, through the air, to the negative electrode, 
on which a part is condensed in the form of graphite. Both carbons 
decrease in size, the positive carbon decreasing more rapidly than the 
negative. 

458. Arc-Light Illumination. — The intense brilliancy 
of the electric arc-light renders it admirably adapted for 
the illumination of light-houses, for large buildings, for 
the streets of cities, or for large areas generally. 

The consumption of the carbon electrodes by combus- 
tion, and the growth of the negative carbon at the expense 
of the positive, render it necessary to employ some means 
by which the carbons may be maintained a constant dis- 
tance apart; for, if they should get too far apart, the cur- 
rent at once ceases and the light goes out, in which case the 
carbons must be brought together again, and slowly sepa- 
rated before the light reappears. The carbons are kept at 
a suitable distance apart by various forms of electric arc- 
lamp mechanism. 

Fig. 181, shows a magnified image of the carbon electrodes, obtained 



298 



NATURAL PHILOSOPHY. 







by means of a suitable lens placed in front of them. The image so 

formed is received on a distant 
screen. A tiny crater or hollow 
may be observed in the end of the 
positive carbon, produced by the 
volatilization of the carbon at this 
point. A tiny nipple, or projec- 
tion of condensed carbon vapor is 
formed on the opposing surface of 
the negative carbon. The intense 
heat of the arc changes the hard 
carbon of the electrode into a soft 
variety of carbon called graphite, 
the material employed in lead-pen- 
cils. The ends of the carbons that 
have been used in arc lamps, may, 
in fact, be used for a short time as 
Fig. I81.-An Image of the Carbon lead-pencils. 
Electrodes. 

459. Incandescent-Lamp 

Illumination. — Arc lamps give so great a quantity of 
light that for inside lighting, such as in an ordinary 
room, a single lamp is more than sufficient. A single 
source of light, however, is apt to produce marked 
shadows. It is, therefore, preferable to employ a number 
of less powerful lights, so that each light may illumine 
the space occupied by the shadow of some other light, 
and thus produce a more nearly uniform illumination. 
This is effected in practice by the use of the incandescent 
lamp. 

The incandescent lamp derives its light from the glowing 
of a fine thread or filament of carbon, that has been ren- 
dered incandescent by the passage of an electric current 
through it. Since carbon readily burns in the air, it is 
necessary to place the carbon inside an exhausted glass 
chamber from which practically all the air has been re- 
moved. The carbon filament is obtained from a carbon- 
aceous paste, that is pressed or squirted through a die 
plate and then carbonized. 



EFFECTS OF AN ELECTRIC CURRENT. 



299 




A form of incandescent electric lamp is shown in Fig. 
182. The carbon filament is mounted inside the lamp 
chamber on a support through which pass the 
leading-in wires that lead the current into 
the lamp chamber. The ends of these wires 
are so electrically connected respectively to 
the two pieces of metal in the base B, of the 
lamp, that the mere insertion of the lamp-base 
into the lamp-socket S, connects the lamp with 
the wires w, w, from which the current is ob- 
tained. 

460. Mechanical Effects. — Usually, the 
electric currents ordinarily employed produce 
no marked mechanical effects. When, how- 
ever, the discharges are sufficiently powerful, 
such as those from a battery of Leyden jars, 
or from a lightning flash, and the path is descent Lamp, 
formed of poor conducting materials, various 
disruptive effects are produced, such as the tearing, frac- 
turing, or fusing of the materials through which the dis- 
charge passes. These results are best seen in the destruc- 
tive effects of a lightning flash. 

461. Physiological Effects. — An electric current, 
passed through a recently killed animal, causes convul- 
sive movements of the muscles, as in life. Passed through 
a living animal it produces similar movements. Its pas- 
sage under suitable conditions is also attended by various 
physiological actions, many of which are favorable to the 
cure of certain diseases. Electricity, however, as a cura- 
tive agent may do more harm than good, and should never 
be employed except by a skilful and intelligent physician. 

462. Chemical Effects. Electrolysis. — When an 
electric current is passed between suitable terminals or 
electrodes, through a compound liquid, or electrolyte, it de- 
composes the molecules of the electrolyte into two con- 



300 NATURAL PHILOSOPHY, 

stituent parts called ions or radicals, which appear at the 
positive and negative electrodes. This decomposition is 
called electrolysis. 

When a substance undergoes electrolysis, its electro-positive ions or 
radicals appear at the negative electrode, and the electro-negative ions 
or radicals, at the positive electrode. In salts of the metals, the metal 
is electro-positive, and the element or elements with which it is com- 
bined are electro-negative. 

463. Electrolysis of Water. Electro-Plating.— 

If two platinum strips be made the electrodes of a vol- 
taic battery, and plunged into water which has been ren- 
dered slightly acid for the purpose of increasing its con- 
ducting power, the current in passing through the solution 
will decompose it, and hydrogen will be given off at the 
negative electrode, and oxygen at the positive electrode. 
If the electrodes be dipped into a solution of any salt of 
a metal, as copper sulphate, the passage of the current 
will decompose the salt, metallic copper will appear at the 
negative electrode, and will be deposited as an adherent 
metallic film on any conducting surface connected there- 
with, and a compound of sulphur will be set free at the 
positive electrode. If the positive electrode be of some 
metal with which the sulphur compound combines; as, for 
example, copper, sulphate of copper will be formed, and 
will thus keep up the strength of the solution. In this way 
we can deposit strong adherent films of metal on the surface 
of any conductor ; for, if the article to be coated be attached 
to the negative electrode of a battery, and dipped into a 
solution of the metal with which we desire to coat the 
article, say copper, and the positive electrode be attached 
to a plate of copper, and also dipped into the liquid, when 
the current passes, the salt will be decomposed, and the 
metal deposited in a uniform layer over the article at the 
negative electrode. This process is called electro-plating, 
and by it articles may be coated with gold, silver, copper, 
iron and other metals. 



EFFECTS OF AN ELECTRIC CURRENT 301 

The wood-cuts in this book were prepared as follows : They were first 
cut in wood by a skilful artist ; the wood-cuts, however, are not used 
directly for printing, as they are expensive and would soon wear out. 
The wooden blocks are pressed into a case filled with a thin sheet of 
beeswax and a perfect impression is thus obtained. This impression is 
then carefully polished with black lead, in order to make it electrically 
conducting, is attached to the negative electrode of a battery, and im- 
mersed in a solution of copper sulphate. By the passage of the cur- 
rent the black lead on the wax is thus covered with a thin sheet of 
copper, which is now the exact reproduction of the figure on the 
wooden block. This film is removed from the wax mould and stiff- 
ened by being backed with stereotype metal, and the form thus obtained 
is used for printing. 

464. Magnetic Effects. — As we have already seen, all 
conductors, no matter what the nature of their substance, 
are surrounded by magnetic flux by the passage of an 
electric current through them, and thereby acquire the 
properties of magnets. 

2 A 







CHAPTER XXVI. 

THE ELECTRIC TELEGRAPH AND OTHER ELECTRIC 
SIGNALING APPARATUS. 

465. The Uses of the Electro-Magnet in Signal- 
ing Apparatus. — The rapidity with which an electro- 
magnet acquires and loses its magnetism, on the making 
or breaking of the electric circuit in which it is placed, is 
utilized in a great variety of signaling apparatus. In all 
these the signals are produced by the to-and-fro movements 
of the armature of an electro-magnet, which produces 
audible sounds, rings bells, moves needles, or operates 
visual signals generally. Among the most important of 
such signaling apparatus are the telegraph, the electro- 
magnetic annunciator, the electric burglar alarm, and call 
apparatus generally. 

466. The Electric Telegraph. — In the electric tele- 
graph, electro-magnets are employed to transmit intelli- 
gence, by the movements of their armatures, on the open- 
ing and closing of their circuits, either by means of the 
movements of a needle over a dial plate, or by the record- 
ing of certain arbitrary characters in the form of dots and 
dashes that represent the letters of the alphabet ; or, more 
commonly in the United States, by means of certain 
sounds which stand for or represent the letters of the 
.alphabet. 

302 



TELEGRAPH AND SIGNALING APPARATUS. 303 

In all systems of telegraphy a line wire or conductor 
connects the two stations between which it is desired to 
establish communication. At each station a device called 
a telegraphic key is provided, for readily making or breaking 
the circuit, together with some form of receiving apparatus 
containing an electro-magnet, either for recording, or for 
rendering visible or audible the signals received. 

467. The Morse Alphabet.— In the following table 
are given the combinations of dots and dashes employed 
in the Morse system to represent the letters of the alpha- 
bet and the numerals : 

a j s --- 

b - k t — 

c - - - 1 u 

d m v- 

e - n w 

f o - - - x 

g p y -■ -- 

h q z — - 

i -- r - -- & 

1 6 



2 7 

3 8 

4 9 

5 



To avoid the running of one letter into another, such as i - - and e -, 

which might be mistaken for s, or for - - - c, a space is left between 

successive letters longer than that between any of the separate dots 
of any single letter, and a still longer space is left between words. 

It will be noticed that two dots, an interval, and one dot stand for c, 
while three dots stand for s ; i, is represented by two dots, while o, is 
represented by a dot, an interval and a dot. Similar differences are 
noticed in the signs for h and y, c and r, z and &. These differences 
are more marked as sounds than as visual signals. Indeed, most teleg- 
raphy by the Morse system is effected by means of sounds. 



304 



NATURAL PHILOSOPHY. 



468. The Morse Sounder. — Originally, the Morse re- 
ceiving telegraphic instrument was an electro-magnetic reg- 
ister, which recorded, in the form of dots and dashes, the 
signals sent over the line, on a band of paper. It was 
found in practice that the operator soon learned to receive 
the telegraphic message by sound, even more readily than 
by means of the recorded dots and dashes received on the 
moving band of paper. This led to the general introduc- 
tion of a form of receiving instrument called the telegraphic 
sounder. A form of Morse sounder, together with a key gen- 
erally employed in Morse telegraphy is shown in Fig. 183. 




Fig. 183.— The Morse Telegraphic Sounder. 

The movements of the armature A, of the electro-magnet 
M, cause a lever L, connected therewith, to produce a series 
of clicks or sounds as it strikes against front and back 
stops placed in the support B. K, is the key handle or 
knob. A switch S> is provided for cutting the key out 
of the circuit when so desired. 

469. The Telegraphic Relay. — In long telegraphic 
lines, when the current reaches the distant end of the 
line, it is too weak to produce an audible signal, or to 
form a satisfactory record. In such cases a form of appa- 
ratus is employed called a telegraphic relay, consisting of 
an electro-magnet whose magnetizing coil contains many 
turns of fine wire. The armature of the relay magnet is 



TELEGRAPH AND SIGNALING APPARATUS. 305 



employed to open and close the circuit of a local battery, 
the current of which operates either the sounder, or the 
recording apparatus. By means of the relay it is possible 
to send telegraphic dispatches across an entire continent. 

470. The Electro-Magnetic Bell, as its name indi- 
cates, is a bell operated by the movements of the armature 
of an electro-magnet. In the form of electro-magnetic 
bell shown in Fig. 184, the armature of the electro-magnet 
is provided with a lever and 
hammer for striking the bell. 
The circuit connections are 
such that when the armature 
is away from the magnet poles, 
and, consequently, the hammer 
does not touch the bell, the cir- 
cuit is completed through the 
coils of the electro-magnet. As 
soon as this occurs the arma- 
ture is attracted and the ham- 
mer strikes the bell. But the 
movement of the armature 
breaks the circuit by moving 
the contact away from w, and 
the armature loses its magne- 
tism. A spring moves the ar- 
mature back again, and closes the circuit at w, so that the 
bell will continue ringing as long as the current is passing 
through the line circuit. 

471. The Electro-Magnetic Annunciator is a form of 
apparatus for operating a visual signal by means of push 
buttons or other keys placed in a circuit. It is usually 
employed in hotels or houses for sending signals from one 
part of the building to another. Push-buttons, or other 
contact keys, placed in a circuit connecting the different 
parts of the building, operate visual signals or annunci- 

20 




Fig, 184— Electro-Magnetic Bell. 



306 



NATURAL PHILOSOPHY. 






ators, placed on a single annunciator board. Each of the 
different parts of the building is connected with a sepa- 
rate electro-magnet, the closing of 
whose circuit sets or moves a visual 
signal, by the movement of its arma- 
ture. In the annunicator shown in 
Fig. 185, the needle connected with 
the parlor has been operated by 
the closing of a push-button in the 
parlor, thus indicating a call from that 
room. An electro-magnetic bell is 
sounded at the same time, so as to 
call attention to the movement of 
the needle. A push at P, is fur- 
nished for re-setting the needle. 

Burglar - Alarm Annunciators are 

operated in a similar manner. In 

this case the burglar is made to 

sound the alarm unconsciously, as he either opens a door 

or window, or walks on contact points placed in mats, or 

on the stairway. 




Fig. 185.— Electro-Magnetic 
Annunciator. 




CHAPTER XXVII. 

INDUCED E. M. F.— DYNAMOS AND MOTORS. 

472. The Galvanometer. — Various means are em- 
ployed in order to ascertain when an electric current is 
flowing through a conductor. One of the simplest of 
these is to bring the conductor near a magnetic needle 
and observe whether or not the needle is deflected. 

Unless, however, the current is powerful, the needle, 
even if delicate, is not visibly deflected. In order to 
magnify the effect of the electric current, it is caused to 
pass through an instrument called a galvanometer. 

The galvanometer consists of many turns of insulated 
wire wound in the form of a flat ring or helix a, Fig. 186. 
A magnetic needle is suspended inside the coil by a fibre 
6, of silk. The current is sent through 
the coil by making it enter at one of 
the binding posts x or y, and pass out 
at the other. Since each turn of the 
wire becomes magnetic during the pas- 
sage of the current, it is evident that 
an increase in the number of turns will 
cause an increase in the attraction or 
repulsion which the coil has for the 
magnetic needle. 

Before using the galvanometer, the coil is 
so placed that the direction of the wire is parallel with the needle ; that 

307 




Fig. 186— A Galvan- 
ometer. 



308 NATURAL PHILOSOPHY. 

is, the coil is placed with the wire extending in a north and south direc- 
tion. On the passage of the current the needle is deflected so as to no 
longer remain parallel to the wire. The strength of the current may 
then be determined from the amount of the deflection of the needle. 

478. Induced Electro-Motive Force. — While mag- 
netic flux is threading or passing through a closed electric 
circuit, it produces an E. M. F. in that circuit, the direction 
of which depends on the direction in which the magnetic 
flux is flowing. For example, if a coil of insulated wire, 
the ends of which are connected to a galvanometer, be 
moved across a magnet pole, so that the flux from the 
magnet passes through the coil, a momentary E. M. F. 
and current will be produced in the coil, as indicated by 
the movement of the galvanometer needle. On reversing 
the motion of the coil, the direction of the E. M. F. and 
current are also reversed. Such an E. M. F. is called 
an induced E, M. F. This variety of induction is some- 
times called dynamo-electric induction. 

Since the induced E. M. F. is due to the passage of magnetic flux 
through the coil, it is evident that it makes no difference whether the 
coil be moved and the magnet be fixed, or the coil be fixed and the 
magnet be moved. In each case an E. M. F. will be induced in the coil, 
provided the motion is such as to cause magnetic flux to pass through 
the coil. 

474. Self- Induction. — When an electric circuit is 
closed, a brief interval of time elapses before the full cur- 
rent strength is established. During all this time the 
magnetic flux which accompanies the current is increas- 
ing. 

If a coil of insulated wire has its terminals connected to a voltaic 
battery, or other electric source, the passage of the electric current 
through it will produce a magnetic flux, which will surround the con- 
ductor and thread through the coil. The passage of this flux through 
the coil will induce an E. M. F. in it. This E. M. F. is in the oppo- 
site direction to the E. M. F. driving the current through the coil. 
When the circuit of the coil is broken, the magnetic flux through it 
disappears, that is, passes through the coil in the opposite direction, 



INDUCED E. M. R— DYNAMOS AND MOTORS. 309 



and, therefore, induces an E. M. F. in the opposite direction to that pro- 
duced when the circuit was closed ; or in the same direction as the 
driving E. M. F. Consequently, the E. M. F. induced on the making 
of the circuit tends to oppose the passage of the current through the 
coil, while that produced on the breaking of the circuit, tends to pro- 
long and strengthen such current. It is for this reason that a bright 
spark is seen on breaking the circuit of a battery in which a long coil of 
insulated w T ire is placed. The spark coil employed in systems of elec- 
tric gas-lighting operates on this principle. E. M. F.'s produced in 
this manner are sometimes called self -induced E. M. E.'s. 

475. Mutual Induction. — The making and breaking 
of the circuit of any conductor carrying a current will 
induce E. M. F.'s in neighboring conductors so placed 
that its magnetic flux threads or passes through their 
coils. This is called mutual induction. 

The action of mutual induction can be shown by means of the appa- 
ratus seen in Fig. 187. A hollow coil A, called the primary coil, of 
moderately stout insulated wire, is connected by wires a, b, c, d, with 

A 




Fig, 187.— Induction by Current Electricity. 



a voltaic cell C. Another hollow coil B, called the secondary coil, 
formed of a considerable length of insulated wire, surrounds the primary 
coiJ. The ends of this coil are connected by means of the wires e and 
/, to a galvanometer G. 

If one of the wires conveying the electric current as d, be raised from 
the mercury in the cup E, so as to break the circuit, and thus cause 
the electricity to stop flowing through the primary coil, a momentary 
current will at once be induced in the secondary coil, as will be shown 
by the movement of the needle of the galvanometer in a certain direc- 
tion. After a few moments, the needle will come to rest, thus showing 



310 NATURAL PHILOSOPHY. 

that the current in the secondary coil has ceased to flow. If now, the 
wire d, be again placed in the mercury cup, so that a current from the 
battery may flow through the primary coil, the galvanometer needle will 
again be deflected, but in the opposite direction to that produced by the 
breaking of the circuit of the primary coil, thus showing that the in- 
duced current produced in the secondary coil, by closing the primary 
circuit, is in the opposite direction to that produced by opening the 
primary circuit. 

In all cases the strength of the induced E. M. F. will depend both 
on the amount of flux passing through the coils, and on the number 
of turns of wire through which it passes. Consequently, the more pow- 
erful the primary current and the magnetism thereby produced, or the 
greater the number of turns in the secondary coil, the greater will be 
the induced E. M. F. 

476. Induction Coils and Transformers. — The form 
of apparatus shown in Fig. 188, is called an induction coil 
or transformer. It is called a transformer because it may- 
transform or change the value of the E. M. F. in the 
primary and secondary circuit. If the number of turns 
in the secondary coil is greater than the number of 
turns in the primary, the value of the E. M. F. induced 
in the secondary circuit will be greater than that in the 
primary circuit, and the transformer is called a step-up 
transformer. If, on the contrary, the number of turns in 
the secondary is smaller than in the primary, the value 
of the induced E. M. F. will be smaller in the secondary 
circuit than in the primary circuit, and the transformer 
will be called a step-down transformer. 

477. The Ruhmkorff Induction Coil. — A common 
form of induction coil, generally called the Ruhmkorff 
coil, from the name of an early maker of this form of coil, 
is shown in Fig. 188. It is a step-up transformer. That is, 
its primary is short and stout, and of but few turns, and 
its secondary a long thin wire of many turns. The ends 
of the secondary are shown at S and S'. The ends of the 
primary are shown at P and P. A device is generally 
employed with this form of coil which automatically 






INDUCED R. M. R— DYNAMOS AND MOTORS. 311 



makes and breaks the circuit. If* the secondary coil is 
long and of very many turns, the induced E. M. F.'s are 
sufficiently powerful to cause a torrent of bluish sparks to 




Fig. 188 — Ruhmkorff Induction Coil. 

pass through the air space or gap between the terminals 
S, £', of the secondary coil. 

478. Dynamo-Electric Machines. — The electric cur- 
rents employed for electric lighting and driving motors 




Fig, 189.— Dynamo-Electric Machine, 

and trolley cars are obtained by means of dynamo-electric 
machines or generators. In these machines, by means of a 



312 



NATURAL PHILOSOPHY. 



steam-engine, a water-wheel or other source of power, a 
number of coils of wire, called the armature, are set into 
rapid rotation between the poles of powerful electro-mag- 
nets. The E. M. F.'s induced by the motion of the arma- 
ture past the poles are constantly changing in direction, 
so that the currents they produce are alternating. The 
number of times per second that such currents change 
their direction, depends on the number of magnet poles 
in the field frame, within which the armature is moving, 
and the speed of rotation. Alternating currents are capa- 
ble of being used directly for arc and incandescent lamps 
and for certain kinds of electric motors. In many forms 

of dynamo, as, for example, in 
that shown in Fig. 189, the cur- 
rents so produced in the armature 
are caused to take the same direc- 
tion, in the circuit outside the ma- 
chine, by means of a contrivance 
called the commutator. The field 
magnets are shown at M and IP, 
and the poles of the magnets at 
N and S, which are north and 
south poles respectively. The 
armature is seen at A, and the com- 
mutator at C. 

479. The Alternating-Current 
Transformer. — Where alternat- 
ing currents are employed, the 
forms of transformers are greatly 
simplified, since no device is re- 
quired to change the direction of 
the current through the primary, 
or to vary its strength. A form 
of transformer is shown in Fig. 190. Here the primary 
and secondary coils are placed parallel to and alongside 




Fig, 190.— Alternating Current 
Transformer, 



INDUCED E. M. E— DYNAMOS AND MOTORS. 313 



each other. In order to insure the greatest amount of 
magnetic tiux passing through the coils they are provided 
with a core of laminated iron which also surrounds the 
coils. Since alternating currents are dangerous, when the 
E. M. F.'s are high, transformers are generally placed out- 
side of buildings, or on high poles, where they cannot be 
reached by the incautious. 

480. The Electric Motor. — If instead of driving the 
armature of the dynamo shown in Fig. 189, by mechanical 
force, a continous electric current be passed through the 
circuit, the armature will revolve and develop mechanical 
power. The dynamo then becomes an electric motor, a de- 
vice by means of which electric energy is transformed into 
mechanical energy. 

The cause of the rotation of the electric motor is the 
mutual action which the magnetic flux of the armature 



f> f^ 




Fig. 191 —Electric Motor. 

and of the field magnets exert on each other, producing 
what is called electro-dynamic force. 

Electric motors are of a great variety of forms. They 
can be operated both by direct and by alternating electric 
currents. The form of motor shown in Fig. 191, is oper- 

2 B 



314 NATUMAL PHILOSOPHY. 

ated by direct or continuous currents. Street-car motors 
are enclosed in dust- and mud-tight boxes in order to pro- 
tect them while in operation. 

481. The Electric Telephone is an instrument by 
means of which the sounds of the human voice, as in 
articulate speech, uttered in any place, can be audibly 
reproduced at places even hundreds of miles distant. The 
telephone consists of a transmitting and receiving instru- 
ment connected by a line wire or conductor. One of the 
simplest forms of telephone is shown in Fig. 192. Here 

E a L 

A B H 

Fig. 192.— Magneto-Electric Telephone Circnit. 

the same form of transmitting and receiving instrument is 
employed at each end of the line. A permanent magnet, 
provided with a coil of insulated wire wrapped around 
it near one end, is connected at one of its ends to a wire 
£1, which passes to a distant station, where it is con- 
nected to one end of a similar coil wrapped around a 
permanent magnet. The other ends of the coils are either 
connected by means of wire ABU, or what serves the 
same purpose, are connected to metallic plates buried in 
the earth at A and H. The circuit so provided is called 
a telephone circuit. The apparent break in the wire E i, 
at a, is intended to represent a great length of wire. 

The method of operation of the instrument is as fol- 
lows ; a circular diaphragm of thin sheet iron is fastened 
at its edges to a mouth-piece P, of wood. On speaking 
into this mouth-piece, the diaphragm is moved in and 
out by the sound-waves. The soft-iron diaphragm being 
near the magnet becomes a magnet by induction, and as 



INDUCED E. M. R— DYNAMOS AND MOTORS. 315 

it is moved towards and from the magnet by sound- 
waves, it produces induced E. M. F.'s and currents in 
the coil of wire, by causing its flux to pass into and out 
of the coil of wire. These currents traversing the circuit, 
flow through the coil at the distant station, and, by chang- 
ing the strength of the magnetism there, cause the dia- 
phragm at P', to pass through movements precisely similar 
to those produced by the sound-waves at P. An ear, 
therefore, placed at P', will hear all that is said at P, even 
though P 7 be hundreds of miles distant from P. One may 
even recognize the peculiarities of the distant speaker's 
voice. 

The manner in which the currents flowing through the coil at P', 
cause movements in its diaphragm may be readily understood by con- 
sidering a single motion of the diaphragm at P, towards and from its 
magnet. Suppose that, by moving it towards the magnet it causes 
an electric current which traverses the telephone circuit and flows 
through the coil at P', so as to increase the magnetism : the diaphragm at 
P / , is at once drawn nearer to its magnet. When now the diaphragm 
at P, moves away from its magnet it produces a current of electricity 
in the opposite direction to that produced by its first movement, which 
current flowing through the coil at P / , decreases the magnetism, when 
the elasticity of the diaphragm at P', causes it at once to move away 
from its magnet. 

Since these movements of the diaphragm correspond precisely to the 
movements of the sound-waves, it will be seen that the diaphragm at P', 
is moved in precisely the same manner as the diaphragm of a person's 
ear would be if he were near the speaker. A person listening at P', 
should, therefore, be able to hear all that is spoken at P. 

The magneto-electric telephone is in reality a dynamo- 
electric machine operated by the voice. The sound-waves - 
striking the diaphragm produce electrical currents which 
flowing through the telephone circuit, reproduce in a dis- 
tant diaphragm the exact movements of the first. Elec- 
trical currents and not sound-waves, pass through the wire 
connecting the telephones. 

The construction of the magneto-telephone will be bet- 



316 



NATURAL PHILOSOPHY. 



ter understood by an inspection of Fig. 193, which repre- 
sents a section of the instrument. The 
magnet H F, has a coil C, at one of its 
ends, the ends of the coil being connected 
to binding screws at x and y. The dia- 
phragm D, is placed near that end of the 
magnet which is surrounded by the coil. 
The centre of the diaphragm i), is directly 
opposite the opening of the mouth-piece P. 
482. The Microphone Transmitter. 
— In practice it is found more satisfactory 
to employ a transmitting instrument of a 
different form from that of the receiving in- 
strument. In such cases a form of transmit- 
ter called the microphone transmitter is em- 
In the microphone transmitter the sound-waves 




Fig. 193 -The Bell 
Telephone, 



ployed. 

are made to vary the electric resistance of a circuit, and 
thereby produce variations in the current of electricity 
which flows through the circuit. These variations are 
made to reproduce in the receiving telephone the sounds 
causing them. Whatever sounds are made near the micro- 
phone, such as talking 
or even breathing, can 
be heard by any one 
listening at the tele- 
phone, even though it 
be several miles dis- 
tant. 

Fig. 194, shows the 
construction of a sim- 
ple form of micro- 
phone transmitter. A 
small rod A B, of hard 
carbon, sharpened at 




Fig, 194.— The Microphone. 



both ends, is loosely placed in small cavities in two other 
carbons C and D, supported as shown, by a piece of thin 



INDUCED E. M. E— DYNAMOS AND MOTORS. 317 



wood E, attached to the base S. The wires a and 6, con- 
nected to the ends of C and D, are placed in the circuit of 
a voltaic battery in which is also placed, a magneto-electric 
telephone. Any variations in the strength of the current 
flowing through the microphone, by producing variations 
in the strength of the telephone magnet, will cause move- 
ments in the diaphragm of the telephone. If a person 
talks anywhere near the microphone, the sound-waves will 
cause movements of the carbons C and D, whereby the 
portions of A B, that are in contact with C and D, are 
varied in exact accordance with the movements of the 
sound-waves ; so that a person listening at the telephone 
will be able to hear distinctly all that is said. 

In actual practice the microphone transmitter usually 
consists of a quantity of loose granulated carbon, so placed 
back of a diaphragm as to vary the resist- 
ance of a circuit on the movements of the 
diaphragm, by the sound-waves. An in- 
duction coil is generally employed in con- 
nection with this form of transmitter. 

So wonderfully sensitive is the microphone that 
the ticking of a watch held near it can be heard by 
a person at the telephone. Even a fly walking over 
the board E, can be heard at the distant telephone. 

The form of telephone apparatus now 
commonly employed is shown in Fig. 
195. A call bell B, is placed in connec- 
tion with the apparatus to call a per- 
son to the phone. The microphone trans- 
mitter is shown at M. The person speaking 
places his mouth near^the microphone and talks against 
the diaphragm, beneath which is placed the granulated 
carbon. The telephone 7, is supported on a hook when 
not in use. 




Fig, 195, 
Telephone Set, 




Aberration, chromatic, of 
lenses, 203; longitudinal 
spherical, 203 ; of spher- 
icity, 203 

Absorption of gases by liq- 
uids and solids, 75 ; of 
heat, 240 ; of heat, selec- 
tive, 241, 242 

Actinic effect, 179 

Actinism, 222 

Action and reaction, 42 

Active conductor, magnetic 
flux of, 291, 292 

Activity, 85 ; of electric 
current, 296 

Adhesion, 17, 67, 69; be- 
tween liquids, 70 ; between 
solids, 69 ; between solids 
and liquids, 70; varieties 
of, 69 

Adhesive attraction, 69 

Adiathermancy, 243 

Affinity, 69; chemical, 17 

Air, buoyancy of, 139 

Alcoholometer, 116 

Alphabet, Morse, telegraph- 
ic, 303 

Alternating - current trans- 
former, 312 

Amalgamation of zinc, 288 

Ampere, 264 

Amplitude of oscillation, 64 

Analysis, solar spectrosco- 
pic, 219; spectrum, 218 

Angle, visual, 191, 192 

Annealing, 77 

Annual variations of earth's 
magnetism, 285 

Annunciator, burglar-alarm, 
306; electro-magnetic, 305 

Apparent size of image, 
207 

Application, point of, 37, 38 

Aqueous humor, 205 

Arc-light illumination, 297 

Archimedes, 109, 139; prin- 
ciple, 109 

Armature of dynamo-elec- 
tric machine, 312 

Arms of lever, 92 

Artesian well, 108 

Atmosphere, 131, 132 

Atmospheric electricity, 
275 ; pressure, illustra- 
tions of, 137; pressure, 
simple experiments in, 
138, 139 

Atoms, 15 

Attraction, adhesive 69 ; 
atomic, 17; chemical, 69 ; 

318 



cohesive, 69; mass, 17; 
molar, 17; molecular, 17; 
molecular, force of, 67 ; 
molecular, forces of, 31 ; 
of gravitation, 17; varie- 
ties of, 17 

Attractions and repulsions, 
electrostatic, 266 ; mag- 
netic, 281 

Atwood's machine, 60, 61 

Ballistic curve, 63 

Balloons, 139 

Barometer, 134, 135 ; ane- 
roid, 135 

Battery of Ley den jars, 274 ; 

Battery or pile, voltaic, 287 ; 
series - connected, 290 ; 
voltaic, 290 

Beam of light, 181 ; or bar, 
tenacity of, 78 

Beating, 174 

Bell, electro-magnetic, 305 ; 
telephone, 316 

Belting, 268 

Benjamin Thomson, 255 

Body, definition of, 11 ; il- 
lumined, 180; luminous, 
180; opaque, 180; trans- 
lucent, 180 ; transparent, 
180 

Boiling-point, influence of 
adhesion on, 254 ; -points, 
table of, 252 

Boyle, 140 

Boyle's or Mariotte's law, 
140 

Boyle's law, experimental 
verification of, 140, 141 

Brittleness, 78 

Broken circuit, 261 

Bunsen, 183 

Buoyancy, 109 ; centre of, 
no; force of, no 

Burglar-alarm annunciator, 
306 

C. G. S. unit of activity, 86; 
unit of force, 86; unit of 
work, 86 ; units, 85 

Caloric, 226 

Calorimeter, 246 

Camera obscura, 210; pho- 
tographing, 209 

Candle power, 183 ; stand- 
^ ard, 183 

Capillarity, 71 ; causes of, 
72, 73 ; examples of, 73 

Capillary phenomena, 71, 
72 ; tube, 72 



Cause and effect, 12 

Causes of vibrations of pen- 
dulum, 146 

Cell, thermo-electric, 290; 
voltaic, 287 

Centigrade thermometer, 
228 

Centimetre -gramme-second 
units, 85 

Centre of buoyancy, no; of 
gravity, 53, 54; of grav- 
ity and point of support, 
54-58 ; gravity, method 
of determining, 54 

Centrifugal force, examples 
of, 47 

Change, chemical, 12 ; phys- 
ical, 12 

Charge, electric, 265 ; nega- 
tive, 267; positive, 267 

Chemical affinity, 17 ; attrac- 
tion, 69 ; effects of elec- 
tric current, 299 

Chemistry, 12 

Chromatics, 214 

Chronograph, 168 

Circuit, electric, 260; hy- 
draulic, 261 ; magnetic, 
280 

Closed circuit, 261 

Cohesion, 17, 67 

Cohesive attraction, 69 

Coil, induction, 310 

Colloids, 74 

Color, cause of, 216; disc, 

215 

Colors, complementary, 217; 
contrast of, 222 

Communicating vessels, 

equilibrium of liquids in, 
107, 108 

Commutator of dynamo- 
electric machine, 312 

Commutators, 287 

Completed circuit, 261 

Components, 43 

Composition of forces, 43 

Compound lever, 92 ; mole- 
cules, 16 

Compressibility of liquids, 
101 

Concave lens, principal fo- 
cus of, 201 

Condensation, 29 

Condenser, 273; of steam 
engine, 258 

Condensing steam engine, 
258 

Conditions or states of mat- 
ter, 29 



INDEX. 



319 



Conductivity of heat, 234, 

235 
Conjugate foci of convex 

lens, 202 
Convection of heat, 237 
Convex lens, principal focus 

of, 201 ; virtual focus of, 

202 
Cores, soft iron, of electro- 
magnets, 293 
Cornea, 205 
Coulumb, 264 
Couple, thermo-electric, 

290 ; voltaic, 287 
Crookes' radiometer, 34 
Crystal, 80 
Crystalline form, 80; lens, 

205 
Crystalloids, 74 
Culinary paradox, 253 
Current, electric, 262 
Curve, ballistic, 63 
Curved mirrors, 189 
Curvilinear motion, 43 
Cylinder of steam engine, 

256 

Dark lines, Fraunhofer's, 
217 

Dead points of engine, 258 

Declination of magnetic 
needle, 285 

Defects of lenses, 202, 203 

Density, 49, 50 

Determination of pitch, 166 

Dialyser, 74 

Dialysis, 74 

Diaphragm of telephone, 
3U 

Diathermancy, 243 

Dielectric, 269 

Diffraction, 220 

Diffusion of gases, 132 ; of 
liquids, 132, 133 

Dip of magnetic needle, 
285 a 

Direction of force, 37, 38 

Directive tendency of mag- 
netic needle, cause of, 284 

Discharge, alternating, 275 ; 
oscillatory, 275 

Dispersion of light, 214; by 
prism, causes of, 216 

Distance, effect of, on gravi- 
tation, 52 ; unit of, 84 

Distinct vision, limits of, 
205 

Divisibility, 26 

Double-fluid voltaic cell, 288 

Double refraction, 221 

Dr. Ohm, 263 

Draught in chimney, cause 
of, 233 

Driven wheel, 96 

Driver of train of wheels, 

95 
Ductility, 76 

Duration of oscillation, 64 
Dynamics, 37 
Dynamo-electric generator, 



311, 312; induction, 308; 
machine, 311, 312 
Dyne, 86 

E. M. F., 260; practical 
unit of, 264 

Earth, shape of, 48 

Earth's magnetism, proba- 
ble cause of, 284 ; varia- 
tions in, 284, 285 

Echoes, 158, 159, 160 

Edison, 176 

Effect, actinic, 179 

Efficiency of machine, 90 

Elastic body, resistance and 
restitution of, 79 

Elasticity, 79 ; limits of, 
80 ; measure of, 80 ; neces- 
sary for vibration, 147 ; of 
form or shape, 79 ; of vol- 
ume or bulk, 79 

Electric activity, unit of, 
296; charge, distribution 
of, 276 ; charges, effects of, 
265, 266 ; charge, influ- 
ence of points on, 270; 
charge, production of, by 
friction, 265 ; current, 262 ; 
current, practical unit of, 
264 ; currents, alternating, 
286 ; currents, direct or 
continuous, 286; quantity, 
unit of, 264 ; telegraph, 
302 

Electricity, nature of, 260 

Electrodes, 299 

Electro-dynamic force, 313 

Electrolysis, 299 ; of water, 
300 

Electrolyte, 287 

Electro-magnet, uses of, in 
signalling apparatus, 302 

Electro-magnetic annunci- 
ator, 305 ; bell, 305 

Electro-magnetism, 291 

Electro-magnets, 292, 293; 
soft-iron cores of, 293 ; 
uses of, 294 

Electromotive force, 260 ; 
force, alternating, 286 ; 
force, direct or continuous, 
286; force, induced, 308; 
force, varieties of, 286 ; 
forces, thermo - electric, 
291 

Electro-negative ions or rad- 
icals, 300 

Electrophorous, 270 

Electro-plating, 300 

Electro-positive ions or rad- 
icals, 300 

Electroscope, 267 

Electrostatic attractions 
and repulsions, 266 

Electrostatics, 266 

Elementary molecules, 16 

Elements, 11 ; of work, 83 

Endless screw, 98 

Endosmometer, 74 

Endosmose, 74 



Endosmotic flow, 74 

Energy, 14, 83; converti- 
bility of, 87; kinetic, 87; 
not created by machines, 
89 ; of vibration, alter- 
nately kinetic and poten- 
tial, 147, 148 ; potential, 
86; radiant, 226, 238; re- 
lation of, to velocity, 87; 
transfer of, 83 ; transfor- 
mation of, 83 

English and French systems 
of weight, 50, 51 ; units 
of measurement, 19, 20, 
21 

Equilibrium, neutral, 55-58 ; 
neutral, of floating bodies, 
in ; of forces, 44 ; of liq- 
uids in communicating 
vessels, 107, 108 ; stable, 
55-58 ; stable, of floating 

• bodies, in ; unstable, 55- 
58 ; unstable, of floating 
bodies, in 

Erg, 86; -per-second, 86 

Escaping jet, reaction of, 
123, 124 

Essential properties of mat- 
ter, 18 

Ether, luminiferous, 178; 
waves, frequencies of, 
179 

Evaporation, 251 ; circum- 
stances influencing, 251 ; 
reduction of temperature 
by, 255 

Exosmose, 74 

Exosmotic flow, 74 

Expansibility, 27 

Expansion of gases, 233 ; 
of liquids, 231; of solids, 
230 

Extension, 18 

Eye, accommodation of, 
206; human, 204; myopic 
or near-sighted, 207 ; pres- 
byopic or far-sighted, 206, 
207 ; pupil of, 205 

Fahrenheit thermome- 
ter, 228 
Falling bodies, laws of, 58, 

59 . 6o 
Far-sightedness, 205 ; how 

remedied, 206 
Field, magnetic, 281 
Floating bodies, no; equi- 
librium of, no; neutral 

equilibrium of, 111 
Flow, 121 ; endosmotic, 74 ; 

exosmotic, 74 ; method 

of ascertaining, 121 ; 

through horizontal pipes, 

122 
Fluids, 31 
Flux, electrostatic, 269; 

magnetic, 279 
Fly-wheel of steam engine, 

256 
Foci, conjoined, 193 



320 



INDEX. 



Focus, shorter conjugate, of 
mirror, 193 

Follower, 96 

Foot-pound, 84 

Foot-pound-per-second, 85 

Force, C. C. S. unit of, 86 ; 
centrifugal, 46 ; centrifu- 
gal, examples of, 47 ; cen- 
tripetal, 47 : direction of, 
37,38; driving, 87; elec- 
tro-dynamic, 313 ; elec- 
tromotive, 260; elements 
of, 37 ; intensity of, 37, 
38 ; magneto-motive, 281 ; 
moving, 87 ; of molecular 
attraction, 67; resolution 
of, 46 ; resultant, 43 ; wa- 
ter-motive, 262 

Forces, component, 43; mo- 
lecular, 30; parallel, 45 

Fork, tuning, 152 

Form, crystalline, 80 

Fraunhofer, 217 

Fraunhofer's dark lines, 
cause of, 220 

Freezing mixtures, 249 

French and English systems 
of weight, 50, 51; units 
of measurement, 19, 20, 
21 

Frequencies, luminous, 219 ; 
of ether waves, 179 

Frequency, 150; effect of, 
on pitch, 165 

Friction, rolling, 24 ; sliding, 
24 

Frictions, 24 

Frictional electricity, ex- 
periments in, 276, 277 

Fundamental tone of string, 
168 

Furnace, electric, 296 

Fusion, laws of, 248 

Galileo, 58 

Galileo's inclined plane, 61 

Galleries, whispering, 160, 
161 

Galvani, 287 

Galvanic pile, 287 

Galvanometer, 307 

Gases, 31 ; diffusion of, 132 ; 
expansion of, 233 ; inco- 
ercible, 30 ; kinetic theory 
of, 130; permanent, 30; 
properties of, 130; tension 
of, 131 

General properties of mat- 
ter, 18 

Generator, dynamo-electric, 
311, 312 

Gramme- degree-centigrade, 
244 

Gravitation, 49 ; attraction 
of, 17; effect of distance 
on, 52 ; effect of mass on, 
51, 52; universal, law of, 
5i . 

Gravity, 13, 17, 49; centre 
°fj 53> 54 » direction of, 



53 ; intensity of, 64, 65 ; 
point of application of, 
53 ; specific, 112 ; varia- 
tions of, 65 

Hard and soft, relative 
terms, 76 

Hardening, 77 

Hardness, 76 

Harmonics, 169 ; of vibrat- 
ing string, 169 

Hearing, limits of, 166 

Heat a form of energy, 226 ; 
absorption of, 240; cause 
of, 225 ; communication 
of, 234; conduction of, 
234 ; emission of, 240, 241 ; 
energy, potential-molecu- 
lar, 247 ; energy, two 
forms of, 226 ; influence 
of, on condition of matter, 
35 ; latent, 247 ; mechan- 
ical equivalent of, 255, 
256 ; of vaporization, 254 ; 
poor conductors of, 236; 
rectilinear propagation of, 
238, 239 ; reflection of, 
240 ; refraction of, 239 ; 
selective radiation of, 241, 
242 ; specific, 245 ; units, 
244 

Heater, electric, 296 

Horizontal pipes, flow of 
liquid through, 122 

Horse-power, 85 

Hydraulics, 101, 119 

Hydrometer, 116 

Hydrostatic press, 103 ; 
press, uses for, 103 ; press- 
ure on base, 104, 105 ; 
pressure on sides of ves- 
sel, 106; upward pressure, 
106 

Hydrostatics, 101 

Illumination, arc-light, 
297; incandescent lamp, 
298 ; intensity of, 182 

Image, real, of mirror, 190; 
virtual, of concave mirror, 
193, 194 ; virtual, of mir- 
ror, 190 

Images, accidental, 222 ; ap- 
parent size of, 207 ; for- 
mation of, by plane mir- 
ror, 189, 190; formed by 
concave mirror, 193, 194 ; 
multiple, 191 

Impenetrability, 18 

Incandescent lamp base, 
29Q ; lamp illumination, 
298 ; lamp socket, 299 

Inclination of magnetic 
needle, 285 

Inclined plane, 96 

Incomplete circuit, 261 

Increase of volume during 
solidification, 250 

Indestructibility, 18 ; of 
matter, 14 



Index of refraction, 196 

Indivisibility, 18 

Induction coil or transform- 
er, 310; coil, Ruhmkorff, 
310 ; dynamo - electric, 
308 ; electrostatic, 268, 
269 ; magnetic, 283 ; mu- 
tual, 309 ; self, 308 

Inertia, 21, 22; a universal 
property of matter, 23 ; 
examples of, 22 

Influence of adhesion on 
boiling-point, 254; of 
pressure on boiling-point, 

253 
Instruments, musical, 174; 

optical, 208, 209 ; stringed, 

174; wind, 175 
Insulators, 264 
Intake of machine, 90 
.Intensity of radiant heat, 

239 ; of sound, effect of 

distance on, 161, 162 
Interference of sound-waves, 

173 • , 

Ions or radicals, 300 ; elec- 
tro-negative, 300 

Iris, 205 

Irradiation, 221 

Isochronism of pendulum, 
64 

Jar, Leyden, 273 
Jet of water, vertical, 123 
Joule, 86, 256 ; per-second, 
86 ; equivalent, 256 

Kaleidoscope, 191 

Kilogramme-metre, 84 

Kinds of matter, 11 

Kinetic and potential energy 
in moving pendulum, 146 ; 
energy, 87; theory of mat- 
ter, 30 

Kinetics, 37 

Lactometer, 116 

Lamp, electric, incandes- 
cent, 298 

Lantern, magic, 210 

Latent heat, 247 

Law, natural, 13 ; of Archi- 
medes, 139 ; Ohm's, 263, 
264 ; of universal gravita- 
tion, 51 

Laws of boiling of liquids, 
252 ; of centrifugal force, 
47; of electrostatic at- 
tractions and repulsions, 
267; of falling bodies, 58, 
59, 60 ; of fusion, 248 ; of 
machines, 90; of motion, 
40 ; of pendulum, 64 ; of 
reflection of light, 188 ; of 
refraction of light, 196; of 
solidification, 248 

Lenses, 199 ; aberrations of, 
202, 203 ; combinations of, 
203 ; defects of, 202, 203 ; 
foci of, 200 



INDEX. 



321 



nature of, 178; pencil of, 
181 ; ray of, 181 ; rccti- 



Lens, achromatic, 203 ; con- 
cave, 200 ; converging, 
200; converging-concavo- 
convex, 200; convex, 200; 
diaphragm of, 203 ; diverg- 
ing, 200 ; diverging-con- 
cavo-convex, 200 ; double 
concave, 200 ; double con- 
vex, 200; plano-concave, 
200; plano-convex, 200 

Lever, 91-93 ; advantages 
of, 92 ; arms of, 92 ; com- 
pound, 92 

Ley den jar, 273 ; -jar bat- 
tery, 274 

Light, absorption of, 187; 
and sound-waves, 178; 
beam of, 181 ; circum- 
stances determining 
amount reflected, 189 ; 
diffraction of, 220; diffu- 
* sion of, 187 ; dispersion 
of, 214 ; double meaning 
of word, 179 ; fluorescent, 
222; interference of, 220 ; 
laws of reflection of, ii 
,178; per 
of, 181 ; 
linear propagation of, 181, 
182; reflection of, 186, 
188; refraction of, 195; 

- sources of, 180 ; undula- 
tory theory of, 179 ; veloc- 
ity of, 186 

Lightning, 275 ; -rods, 275, 
276 

Limits of elasticity, 80 

Liquefaction, 29 

Liquid pressure as a me- 
chanical power, 102 

Liquids, 29, 31 ; cohesion 
of, 68 ; compressibility of, 
101 ; diffusion of, 70, 132, 
133; effect of air pressure 
on, 33 ; expansion of, 231 ; 
free or upper surface of, 
32 ; mixture of, 70 ; mo- 
bile, 32; solution of, 70; 
viscid, 32 ; viscous, 32 

Litre, 20 

Load, 87 

Lodestone, 281 

Luminiferous ether, 178 

Luminous effects of electric 
current, 297 

M. M. F., 281 

Machine, 87; compound, 
98; dynamo-electric, 311, 
312 ; efficiency of, 90 ; elec- 
tric, 271, 272 ; electro- 
static induction, 273 ; in- 
take of, 90 ; output of, 90 ; 
plate, electric, 272 ; sim- 
ple, 88; Topler-Holtz, 
272, 273 

Machines, advantages gain- 
ed by, 90 

Made circuit, 261 

Magnetic circuit, 280; ef- 

21 



fects of electric current, 
301 ; field, 281 ; flux, 279 ; 
flux of active conductor, 
291, 292; flux-paths, 279; 
needle, 278 ; needle, de- 
clination of, 285 

Magnetism, 278; electro-, 
291 ; permanent, 283 ; 
temporary, 283 ; theory 
of, 281, 282 

Magnetization, 282 

Magneto-electric telephone 
circuit, 314 

Magneto-motive force, 281 

Magnets, electro-, 292, 293 ; 
natural, 281 

Malleability, 76 

Mariotte's or Boyle's law, 
140 

Mass, 39, 40; effect of, on 
mutual attraction, 51, 52 

Masses, 16, 17 

Matter, 9 ; changes in, 12 ; 
dimensions of, 10 ; essen- 
tial properties of, 18; gen- 
eral properties of, 18; in- 
destructibility of, 14 ; in- 
fluence of heat on, 35 ; 
kinds of, 11; particular 
properties of, 18 ; proper- 
ties of, 11; radiant, 34; 
specific properties of, 18 ; 
states or conditions of, 
29; ultra-gaseous, 29; ul- 
tra-gaseous or radiant 
state of, 34 

Maximum density of water, 
temperature of, 232 ; ten- 
sion of vapor, 251 

Measurement, units of, 19, 
20, 21 

Mechanical effects of elec- 
tric current, 299 ; equiva- 
lent of heat, 255, 256 ; 
powers, 91-98 

Medium, necessity of, for 
transmission of sound, 155 

Meniscus, 200 

Method of mixture for de- 
termination of specific 
heats, 246 

Metre, 19 

Microphone, 316 ; transmit- 
ter, 316, 317 

Microscope, compound, 
211; object lens or glass 
of, 211 ; simple, 209 

Mirror, 189; centre of curv- 
ature of, 193 ; concave, 
192 ; convex, 192 ; focus 
of, 192, 193 ; longer conju- 
gate focus of, 193 

Mirrors, plane or curved, 
189 

Mobility, 23 

Molecular attraction, forces 
of, 31, 67; forces, 30; re- 
pulsion, forces of, 31 

Molecules, 15, 16; com- 
pound, 16; elementary, 



16 ; mean-free paths of, 

Momentum, 41 

Morse sounder, 303 ; tele- 
graphic alphabet, 303 

Motion, curvilinear, 43; 
first law of, 40 ; laws of, 
40 ; rectilinear, 43 ; re- 
sistances to, 24 ; result- 
ant, 43 ; rotary, 43 ; sec- 
ond law of, 40 ; third law 
of, 42 ; uniform, 42 ; uni- 
formly accelerated, 42 ; 
uniformly retarded, 42 ; 
uniformly varied, 42 ; va- 
ried, 42 ; varieties of, 42 

Motor, electric, 313 

Moving pendulum, kinetic 
and potential energy in, 
146 

Multiple echoes, 160 

Musical sounds and noises, 
distinction between, 163 ; 
sounds, characteristics of, 
164 

Mutual induction, 309 

Natural philosophy, 12, 

13 
Near-sightedness, 205 ; how 

remedied, 206 
Negative pole or terminal 

of voltaic cell, 288 
Nerve, optic, 204 
Newton, 51 
Noises, continuous, 163 ; 

momentary, 163 
Non-condensing steam en- 
gine, 258 
Normal human eye, 206, 

207 
North - seeking magnetic 

pole, 279 

Observation, 13 

Ohm, 263 

Ohm's law, 263, 264 

Open circuit, 261 

Oscillation, amplitude of, 
64 ; duration of, 64 ; or vi- 
bration, 64; time of, 64 

Osmose, 73 

Output of machine, 90 

Overtones, 169 ; of vibrat- 
ing string, 169 

Parallel forces, 45 
Parallelogram of forces, 44, 

45 

Particular properties of mat- 
ter, 18 

Pascal, 102 

Pascal's law of transmis- 
sion of liquid pressure, 
102 

Pencil of light, 181 

Pendulum, 63; isochronism 
of, 64 ; laws of, 64 

Penumbra, 185 

Perpetual motion, 99 



322 



INDEX. 



Phenomena, capillary, 71, 
72 

Phenomenon, 12 

Phonautograph, 168 

Phonograph, 176, 177 

Phosphorescence, 187 

Photometer, 183 ; Bunsen's 
183 

Physics, 12 

Physiological effects of elec- 
tric current, 299 

Pile, galvanic, 287 ; or bat- 
tery, voltaic, 287 

Pipe, organ, 175 

Pitch, 165 ; determination 
of, 166 ; effect of frequency 
on, 165 ; graphical deter- 
mination of, 167, 168 

Plane mirrors, 189 

Pneumatics, 101, 130 

Point of application of force, 
37> 38 ; of application of 
gravity, 53 

Points, influence of, on elec- 
tric charge, 270 

Points, magnetic, 279 ; plus 
and minus, of source, 261 

Pole, negative, magnetic, 
279 ; north-seeking, 279 ; 
positive, magnetic, 279; 
south-seeking, magnetic, 
279 

Pores, 16 ; inter-atomic, 26 ; 
inter-molar, 26 ; inter-mo- 
lecular, 26 

Porosity, 26 

Positive pole of source, 261 ; 
pole or terminal of voltaic 
cell, 288 

Potential energy, 86 

Pound-degree Fahrenheit, 
244 

Power, 85 ; horse, 85 ; unit 
of, 85 

Powers, mechanical, 91-98 

Practical unit of E. M. F., 
264 ; unit of electric cur- 
rent, 264; unit of electric 
resistance, 264 

Pressure, atmospheric, 133; 
effect of, on density of gas, 
140, 141 ; effect of, on vol- 
ume of a gas, 140, 141 

Prism, formation of spec- 
trum by, 214 

Prisms, 198 

Projectile, range of, 62 

Projectiles, 61 

Properties of gases, 130; of 
matter, 11 

Pulley, 94; compound, 95; 
fixed, 94 ; movable, 94 

Pump, air, 136; force, for 
water, 143 ; suction for 
water, 142 

Pupil of eye, 205 

Radiant energy, 238 ; 
heat, intensity of, 239 ; or 
ultra-gaseous state, 34 



Radiation, 179; of heat, 
238 ; secondary, of heat, 
240 

Radicals or ions, 17, 300 

Radiograph, 223 

Radiometer, 34 

Rainbow, 217 

Range, 62 ; of projectile, 
62 ; or stove, electric, 296 

Rate-of-doing work, 85 

Ray of light, 181 

Rays, Rontgen, 223 ; visu- 
al, 191 

Reaction of water jet, 123, 
124; vase, 124 

Real image of concave mir- 
ror, 194 

Receiver, exhausted, 136 

Rectilinear motion, 43 

Reflection of heat, 240 ; of 
light, laws of, 188 

Refracting media, shapes 
of, 198 

Refraction, effect of, on ap- 
parent position of objects, 
197, 198; index of, 196; 
of heat, 239 ; of light, 
laws of, 196 

Reluctance, magnetic, 281 

Repulsion, molecular forces 
of, 31 

Resistance, 87 ; electric, 
263 ; hydraulic, 262 ; mag- 
netic, 281 

Resonance, 170, 171; ex- 
amples of, 172, 173 

Resonators, 171 

Resultant motion, 43 

Resultants, 43 

Rivers, velocity of, 123 

Rontgen, 223 ; rays, 223 

Ruhmkorff, 310; induction 
coil, 310 

Rumford, 255 

Sand-blast process, 77 

Saturated vapor, 251 

Saturation, magnetic, 282 

Savart's wheel, 165, 167 

Screw, 97 ; or worm, 98 ; 
principle of, 97 

Secondary radiation of heat, 
240; waves, 220 

Selective absorption of 
heat, 241, 242; absorp- 
tion of heat, cause of, 
242, 243 ; radiation of 
heat, 241, 242 

Self-induction, 308 

Series - connected battery, 
290 

Shadow, acoustic, 158 ; com- 
plete, 185 ; partial, 185 

Shadows, 185 

Shafting, 258 

Shapes of refracting media, 
198 

Simple machine, 88 ; ma- 
chine, principle of opera- 
tion of, 88 



Single-fluid voltaic cell, 288 

Siphon, 142 

Siren, 166, 167 

Slide valve of steam-engine, 
256 

Small apertures, formation 
of images by, 183, 184 

Softening, 77 

Solar spectroscopic analy- 
sis, 219 

Solidification, 35 ; laws of, 
248 

Solids, 29, 31 ; expansion 
of, 230; properties pecu- 
liar to, 76 ; solution of, by 
liquids, 70 

Sound, cause of, 152 ; double 
meaning of word, 153 ; 
effect of temperature on 
velocity of, 157; intensity 
or loudness of, 164 ; qual- 
ity of, 168 ; quality or 
timbre, 164 ; reflection of, 
158; refraction of, 161; 
timbre, 168 ; tone or pitch 
of, 154; transmission of, 
x 54> *55 ; velocity of, in 
air, 156, 157; waves, in- 
terference of, 173 ; waves, 
nature of, 153 

Sounds, high or low, 165 ; 
shrill or grave, 165 

Sounder, Morse, 303 

Source, poles or terminals 
of, 261 

Sources, electric, 260, 286 

South - seeking magnetic 
pole, 279 

Specific gravities, table of, 
116; gravity, 122; grav- 
ity bottle, 115 ; gravity, 
general method of deter- 
mining, 112, 113; heat, 
245 ; heat of water, 247 ; 
heats, table of, 245; prop- 
erties of matter, 18 

Spectacles, concave, use of, 
206 ; convex, use of, 206 

Spectroscope, 218, 219 

Spectrum, 214 

Speculum, 189 

Sphericity, aberration of, 
203 

Statics, 37 

Steam boiler, 256; chest, 
256 ; engine, 256 ; engine, 
condensing, 258 ; engine, 
non-condensing, 258 

Step-down transformer, 310 

Step-up transformer, 310 

Stereoscope, 213 

Stokes's law, 219 

Storms, electric, 285 ; mag- 
netic, 285 

Stranded conductor, 276 

Stretched cord, vibrations 
of, 150, 151 

String, fundamental tone of, 
168 

Sublimation, 251 



INDEX. 



323 



Substances, n ; compound, 
ii ; elementary, n ; melt- 
ed or fused, 35 ; refrac- 
tory, 35; varieties of, 11 

Sun spots, 285 

Surface of liquid at rest, 
107 ; tension, 72 

Sympathetic vibrations, 
169, 170 

Systems of weight, French 
and English, 50, 51 

Table of boiling-points, 
252; of heat conductivi- 
ties, 236 ; of melting- and 
fusing-points of various 
substances, 249; of spe- 
cific gravities, 116; of 
specific heats, 245 ; of 
tenacities, 79 ; of veloci- 
ties, 29 

Telegraph, 302 

Telegraphic key, 303 ; re- 
ceiving apparatus, 303 ; 
relay, 304, 305 ; sounder, 
3<H 

Telephone, electric, 314 

Telescope, 211 ; eye lens of, 
211; object lens of, 211; 
reflecting, 212 ; refract- 
ing, 212 

Temper, drawing the, 77 

Temperature, 227; effect of, 
on velocity of sound, 157; 
effect of, on volume and 
density of a gas, 139 

Tenacities, table of, 79 

Tenacity, 78 

Tension, surface, 72 

Terminals or poles of source, 
261 

The senses, 10 

Theorem of Torricelli, 120 

Thermal effects of electric 
current, 296 

Thermo - electric couple, 
290 ; -electric electromo- 
tive forces, 291 

Thermometer, 227; Centi- 
grade, 228 ; construction 
of, 228 ; Fahrenheit, 228 ; 
graduation of, 228 

Thermo-pile of battery, 290 

Thunder, 275 

Time, 38, 39 ; of oscillation, 
64 

Topler-Holtz machine, 272, 

273 
Torricellii, 120, 134 
Torricelli's experiment, 134 
Trains of wheel-work, 95 



Transfer of energy, 83 

Transformation of energy, 
83 

Transformer, 310 ; alternat- 
ing-current, 312 ; step- 
dovun, 310; step-up, 310 

Translucent body, 180 

Trumpet, ear, 165 ; speak- 
ing, 164 _ 

Turbine, inside, 128 ; out- 
side, 128 ; water-wheel, 
127, 128 

Twilight, cause of, 197 

Ultra-gaseous matter, 
29 ; -gaseous or radiant 
state, 34 

Umbra, 185 

Undulatory theory of light, 
179 

Uniform motion, 42 

Unit of activity, C. G. S., 
86 ; of distance, 84 ; of 
electric activity, 296 ; of 
electric quantity, 264 ; of 
power, 85 ; of work, 84. 

Units, C. G. S., 85; centi- 
metre-gramme-second, 85; 
heat, 244 ; of measure- 
ment, 19, 20, 21 ; of meas- 
urement, English, 19, 20, 
21 ; of measurement, 
French, 19, 20, 21 

Universal gravitation, law 
of, 51 

Uses of electro-magnet in 
signalling apparatus, 302 ; 
of electro-magnets, 294 

Vapor, saturated, 251 

Vapors, 29 

Vaporization, 251 ; heat of, 

254 

Variation of magnetic nee- 
dle, 285 

Variations, annual, of 
earth's magnetism, 285 ; 
irregular, of earth's mag- 
netism, 284 ; of earth's 
magnetism, 284 ; secular, 
of earth's magnetism, 285 

Velocities of all ordinary 
sounds the same, 158 

Velocity, 39 ; of light, 186 

Vertical water-jet, 123 

Vibrating bodies, energy ex- 
pended by, 147 

Vibration, amplitude of, 
146; frequency of, 150; 
or oscillation, 64 ; period 
of, 146 



Vibrations, longitudinal, 
150; nature of, 145; of 
pendulum, causes of, 146 ; 
sympathetic, 169, 170; 
torsional, 150 ; transverse, 
150 

Virtual focus of convex 
lens, 202 

Visible object, apparent po- 
sition of, 190 

Vision, binocular, 213 ; limit 
of distinct, 205 

Vitreous humor, 205 

Volt, 264 ; ampere, 296 

Volta, 264, 287 

Voltaic battery, 290; cell, 
bichromate, 289; cell, 
bluestone gravity, 289 ; 
cell, Bunsen, 289; Le- 
chanche, 290 ; cell, single 
fluid, 288 

Von Kleist, 273 

Water, electrolysis of, 300 ; 
motive force, 262 ; spe- 
cific heat of, 247 ; tem- 
perature of maximum 
density of, 232 : wheel, 
breast, 126, 127 ; wheel, 
overshot, 126 ; wheel, 
transference of energy of 
running water to, 124; 
wheel, turbine, 127, 128 ; 
wheel, undershot, 125; 
wheels, 124 
I Watt, 86, 296 

Wave motion, nature of, 
i45 

Waves of condensation and 
rarefaction, 154 ; of light 
and sound, 178 ; second- 
ary, 220; velocity of, 150 

Wedge, 97 

Weight, 26, 49, 87 ; English 
and French systems of, 
50, 51 

Welding, 68 

Wetting, 77 

Wheel and axle, 92 ; -work, 
trains of, 95 

Windlass, 93 

Winds, cause of, 233 

Wollaston, 217 

Work, 82, 87; C. G. S., 
unit of, 86; elements of, 
83; practical unit of, 86; 
rate-of-doing, 85 ; unit of, 
84 

Worm or screw, 98 

^-picture, 223 ; -rays, 223 







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